{"id":931,"date":"2017-10-19T22:17:19","date_gmt":"2017-10-19T22:17:19","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstats1xmaster\/?post_type=back-matter&p=931"},"modified":"2017-10-19T22:17:19","modified_gmt":"2017-10-19T22:17:19","slug":"appendix-g-notes-for-the-ti-83-83-84-84-calculators","status":"publish","type":"back-matter","link":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/back-matter\/appendix-g-notes-for-the-ti-83-83-84-84-calculators\/","title":{"raw":"Appendix G: Notes for the TI-83, 83+, 84, 84+ Calculators","rendered":"Appendix G: Notes for the TI-83, 83+, 84, 84+ Calculators"},"content":{"raw":"

Quick Tips<\/h1>\n

Legend<\/span><\/p>\n\n

\n
\"A<\/span>represents a button press<\/div>\n
[ ]<\/code> represents yellow command or green letter behind a key<\/div>\n
< ><\/code> represents items on the screen<\/div>\n<\/div>\n

To adjust the contrast<\/span>Press \"2nd<\/span>, then hold \"arrow<\/span>to increase the contrast or \"arrow<\/span>to decrease the contrast.<\/p>\n

To capitalize letters and words<\/span>Press \"alpha<\/span>to get one capital letter, or press \"2nd<\/span>, then \"alpha<\/span>to set all button presses to capital letters. You can return to the top-level button values by pressing \"alpha<\/span>again.<\/p>\n

To correct a mistake<\/span>If you hit a wrong button, just hit \"clear<\/span>and start again.<\/p>\n

To write in scientific notation<\/span>Numbers in scientific notation are expressed on the TI-83, 83+, 84, and 84+ using E notation, such that...<\/p>\n\n

\n
4.321 E 4 = 4<\/span>.321<\/span>\u00d7<\/span>10<\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
4.321 E \u20134 = 4<\/span>.321<\/span>\u00d7<\/span>10<\/span><\/span>\u20134<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<\/div>\n

To transfer programs or equations from one calculator to another:<\/span>Both calculators:<\/strong> Insert your respective end of the link cable cable and press \"2nd<\/span>, then [LINK]<\/code>.<\/p>\n

Calculator receiving information:<\/span><\/p>\n\n

\n
Use the arrows to navigate to and select <RECEIVE><\/code><\/div>\n
Press \"enter<\/span>.<\/div>\n<\/div>\n

Calculator sending information:<\/span><\/p>\n\n

\n
Press appropriate number or letter.<\/div>\n
Use up and down arrows to access the appropriate item.<\/div>\n
Press \"enter<\/span>to select item to transfer.<\/div>\n
Press right arrow to navigate to and select <TRANSMIT><\/code>.<\/div>\n
Press \"enter<\/span>.<\/div>\n<\/div>\n
NOTE<\/div>\n<\/header>

ERROR 35 LINK generally means that the cables have not been inserted far enough.<\/p>\n\n<\/section><\/div>\n

Both calculators:<\/strong> Insert your respective end of the link cable cable Both calculators: press \"2nd<\/span>, then [QUIT]<\/code> to exit when done.<\/p>\n\n<\/section>

Manipulating One-Variable Statistics<\/h1>\n
NOTE<\/div>\n<\/header>

These directions are for entering data with the built-in statistical program.<\/p>\n\n<\/section><\/div>\n
Sample Data<\/span>We are manipulating one-variable statistics.<\/caption>\n
Data<\/th>\nFrequency<\/th>\n<\/tr><\/thead>
\u20132<\/td>\n10<\/td>\n<\/tr>
\u20131<\/td>\n3<\/td>\n<\/tr>
0<\/td>\n4<\/td>\n<\/tr>
1<\/td>\n5<\/td>\n<\/tr>
3<\/td>\n8<\/td>\n<\/tr><\/tbody><\/table>

To begin:<\/span><\/p>\n\n

\n
\n

Turn on the calculator.<\/p>\n\n

\n\"on<\/span>\n\n<\/div>\n
\n

Access statistics mode.<\/p>\n\n

\n\"stat<\/span>\n\n<\/div>\n
\n

Select <4:ClrList><\/code> to clear data from lists, if desired.<\/p>\n\n

\n\"number<\/span>, \"enter<\/span>\n\n<\/div>\n
\n

Enter list [L1]<\/code> to be cleared.<\/p>\n\n

\n\"2nd<\/span>, [L1]<\/code> , \"enter<\/span>\n\n<\/div>\n
\n

Display last instruction.<\/p>\n\n

\n\"2nd<\/span>, [ENTRY]<\/code>\n\n<\/div>\n
\n

Continue clearing remaining lists in the same fashion, if desired.<\/p>\n\n

\n\"arrow<\/span>, \"2nd<\/span>, [L2]<\/code> , \"enter<\/span>\n\n<\/div>\n
\n

Access statistics mode.<\/p>\n\n

\n\"stat<\/span>\n\n<\/div>\n
\n

Select <1:Edit . . .><\/code><\/p>\n\n

\n\"enter<\/span>\n\n<\/div>\n
\n

Enter data. Data values go into [L1]<\/code>. (You may need to arrow over to [L1]<\/code>).<\/p>\n\n

\n
\n

Type in a data value and enter it. (For negative numbers, use the negate (-) key at the bottom of the keypad).<\/p>\n\n

\n\"negative<\/span>, \"number<\/span>, \"enter<\/span>\n\n<\/div>\n
Continue in the same manner until all data values are entered.<\/div>\n<\/div>\n<\/div>\n
\n

In [L2]<\/code>, enter the frequencies for each data value in [L1]<\/code>.<\/p>\n\n

\n
\n

Type in a frequency and enter it. (If a data value appears only once, the frequency is \"1\").<\/p>\n\n

\n\"number<\/span>, \"enter<\/span>\n\n<\/div>\n
Continue in the same manner until all data values are entered.<\/div>\n<\/div>\n<\/div>\n
\n

Access statistics mode.<\/p>\n\n

\n\"stat<\/span>\n\n<\/div>\n
Navigate to <CALC><\/code>.<\/div>\n
\n

Access <1:1-var Stats><\/code>.<\/p>\n\n

\n\"enter<\/span>\n\n<\/div>\n
\n

Indicate that the data is in [L1]<\/code>...<\/p>\n\n

\n\"2nd<\/span>, [L1]<\/code> , \"comma<\/span>\n\n<\/div>\n
\n

...and indicate that the frequencies are in [L2]<\/code>.<\/p>\n\n

\n\"2nd<\/span>, [L2]<\/code> , \"enter<\/span>\n\n<\/div>\n
The statistics should be displayed. You may arrow down to get remaining statistics. Repeat as necessary.<\/div>\n<\/div>\n<\/section>

Drawing Histograms<\/h1>\n
NOTE<\/div>\n<\/header>

We will assume that the data is already entered.<\/p>\n\n<\/section><\/div>\n

We will construct two histograms with the built-in STATPLOT application. The first way will use the default ZOOM. The second way will involve customizing a new graph.<\/p>\n\n

  1. \n

    Access graphing mode.<\/p>\n\n

    \n\"2nd<\/span>, [STAT PLOT]<\/code><\/li>\n\t
  2. \n

    Select <1:plot 1><\/code> to access plotting - first graph.<\/p>\n\n

    \n\"enter<\/span><\/li>\n\t
  3. \n

    Use the arrows navigate go to <ON><\/code> to turn on Plot 1.<\/p>\n\n

    \n<ON><\/code> , \"enter<\/span><\/li>\n\t
  4. Use the arrows to go to the histogram picture and select the histogram. \"enter<\/span><\/li>\n\t
  5. Use the arrows to navigate to <Xlist><\/code>.<\/li>\n\t
  6. \n

    If \"L1\" is not selected, select it.<\/p>\n\n

    \n\"2nd<\/span>, [L1]<\/code> , \"enter<\/span><\/li>\n\t
  7. Use the arrows to navigate to <Freq><\/code>.<\/li>\n\t
  8. \n

    Assign the frequencies to [L2]<\/code>.<\/p>\n\n

    \n\"2nd<\/span>, [L2]<\/code> , \"enter<\/span><\/li>\n\t
  9. \n

    Go back to access other graphs.<\/p>\n\n

    \n\"2nd<\/span>, [STAT PLOT]<\/code><\/li>\n\t
  10. Use the arrows to turn off the remaining plots.<\/li>\n\t
  11. Be sure to deselect or clear all equations before graphing.<\/strong><\/li>\n<\/ol>

    To deselect equations:<\/span><\/p>\n\n

    \n
    \n

    Access the list of equations.<\/p>\n\n

    \n\"Y=<\/span>\n\n<\/div>\n
    \n

    Select each equal sign (=).<\/p>\n\n

    \n\"arrow<\/span>\"arrow<\/span>\"enter<\/span>\n\n<\/div>\n
    Continue, until all equations are deselected.<\/div>\n<\/div>\n

    To clear equations:<\/span><\/p>\n\n

    \n
    \n

    Access the list of equations.<\/p>\n\n

    \n\"Y=<\/span>\n\n<\/div>\n
    \n

    Use the arrow keys to navigate to the right of each equal sign (=) and clear them.<\/p>\n\n

    \n\"arrow<\/span>\"arrow<\/span>\"clear<\/span>\n\n<\/div>\n
    Repeat until all equations are deleted.<\/div>\n<\/div>\n

    To draw default histogram:<\/span><\/p>\n\n

    \n
    \n

    Access the ZOOM menu.<\/p>\n\n

    \n\"ZOOM<\/span>\n\n<\/div>\n
    \n

    Select <9:ZoomStat><\/code>.<\/p>\n\n

    \n\"number<\/span>\n\n<\/div>\n
    The histogram will show with a window automatically set.<\/div>\n<\/div>\n

    To draw custom histogram:<\/span><\/p>\n\n

    \n
    Access window mode to set the graph parameters.\n
    \n\"window<\/span>\n\n<\/div>\n
    \n
    \n
    X<\/span>min<\/span><\/span><\/span>=<\/span>\u20132.5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
    X<\/span>max<\/span><\/span><\/span>=<\/span>3.5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
    X<\/span>s<\/span>c<\/span>l<\/span><\/span><\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span> (width of bars)<\/div>\n
    Y<\/span>min<\/span><\/span><\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
    Y<\/span>max<\/span><\/span><\/span>=<\/span>10<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
    Y<\/span>s<\/span>c<\/span>l<\/span><\/span><\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span> (spacing of tick marks on y<\/em>-axis)<\/div>\n
    X<\/span>r<\/span>e<\/span>s<\/span><\/span><\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<\/div>\n<\/div>\n
    Access graphing mode to see the histogram.\n
    \n\"graph<\/span>\n\n<\/div>\n<\/div>\n

    To draw box plots:<\/span><\/p>\n\n

    \n
    \n

    Access graphing mode.<\/p>\n\n

    \n\"2nd<\/span>, [STAT PLOT]<\/code>\n\n<\/div>\n
    \n

    Select <1:Plot 1><\/code> to access the first graph.<\/p>\n\n

    \n\"enter<\/span>\n\n<\/div>\n
    \n

    Use the arrows to select <ON><\/code> and turn on Plot 1.<\/p>\n\n

    \n\"enter<\/span>\n\n<\/div>\n
    \n

    Use the arrows to select the box plot picture and enable it.<\/p>\n\n

    \n\"enter<\/span>\n\n<\/div>\n
    Use the arrows to navigate to <Xlist><\/code>.<\/div>\n
    \n

    If \"L1\" is not selected, select it.<\/p>\n\n

    \n\"2nd<\/span>, [L1]<\/code> , \"enter<\/span>\n\n<\/div>\n
    Use the arrows to navigate to <Freq><\/code>.<\/div>\n
    \n

    Indicate that the frequencies are in [L2]<\/code>.<\/p>\n\n

    \n\"2nd<\/span>, [L2]<\/code> , \"enter<\/span>\n\n<\/div>\n
    \n

    Go back to access other graphs.<\/p>\n\n

    \n\"2nd<\/span>, [STAT PLOT]<\/code>\n\n<\/div>\n
    Be sure to deselect or clear all equations before graphing<\/strong> using the method mentioned above.<\/div>\n
    \n

    View the box plot.<\/p>\n\n

    \n\"graph<\/span>, [STAT PLOT]<\/code>\n\n<\/div>\n<\/div>\n<\/section>

    Linear Regression<\/h1>\n

    Sample Data<\/h2>\n

    The following data is real. The percent of declared ethnic minority students at De Anza College for selected years from 1970\u20131995 was:<\/p>\n\n
    The independent variable is \"Year,\" while the independent variable is \"Student Ethnic Minority Percent.\"<\/caption>\n
    Year<\/th>\nStudent Ethnic Minority Percentage<\/th>\n<\/tr><\/thead>
    1970<\/td>\n14.13<\/td>\n<\/tr>
    1973<\/td>\n12.27<\/td>\n<\/tr>
    1976<\/td>\n14.08<\/td>\n<\/tr>
    1979<\/td>\n18.16<\/td>\n<\/tr>
    1982<\/td>\n27.64<\/td>\n<\/tr>
    1983<\/td>\n28.72<\/td>\n<\/tr>
    1986<\/td>\n31.86<\/td>\n<\/tr>
    1989<\/td>\n33.14<\/td>\n<\/tr>
    1992<\/td>\n45.37<\/td>\n<\/tr>
    1995<\/td>\n53.1<\/td>\n<\/tr><\/tbody><\/table>
    Student Ethnic Minority Percentage<\/div>\n\"This<\/span>\n\n
    By hand, verify the scatterplot above.<\/figcaption><\/figure>
    NOTE<\/div>\n<\/header>

    The TI-83 has a built-in linear regression feature, which allows the data to be edited.The x<\/em>-values will be in [L1]<\/code>; the y<\/em>-values in [L2]<\/code>.<\/p>\n\n<\/section><\/div>\n

    To enter data and do linear regression:<\/span><\/p>\n\n

    \n
    \n

    ON Turns calculator on.<\/p>\n\n

    \n\"on<\/span>\n\n<\/div>\n
    Before accessing this program, be sure to turn off all plots.\n
    \n
    \n

    Access graphing mode.<\/p>\n\n

    \n\"2nd<\/span>, [STAT PLOT]<\/code>\n\n<\/div>\n
    \n

    Turn off all plots.<\/p>\n\n

    \n\"number<\/span>, \"enter<\/span>\n\n<\/div>\n<\/div>\n<\/div>\n
    Round to three decimal places. To do so:\n
    \n
    \n

    Access the mode menu.<\/p>\n\n

    \n\"mode<\/span>, [STAT PLOT]<\/code>\n\n<\/div>\n
    \n

    Navigate to <Float><\/code> and then to the right to <3><\/code>.<\/p>\n\n

    \n\"arrow<\/span>\"arrow<\/span>\n\n<\/div>\n
    \n

    All numbers will be rounded to three decimal places until changed.<\/p>\n\n

    \n\"enter<\/span>\n\n<\/div>\n<\/div>\n<\/div>\n
    \n

    Enter statistics mode and clear lists [L1]<\/code> and [L2]<\/code>, as describe previously.<\/p>\n\n

    \n\"stat<\/span>, \"number<\/span>\n\n<\/div>\n
    \n

    Enter editing mode to insert values for x<\/em> and y<\/em>.<\/p>\n\n

    \n\"stat<\/span>, \"enter<\/span>\n\n<\/div>\n
    Enter each value. Press \"enter<\/span>to continue.<\/div>\n<\/div>\n

    To display the correlation coefficient:<\/span><\/p>\n\n

    \n
    \n

    Access the catalog.<\/p>\n\n

    \n\"2nd<\/span>, [CATALOG]<\/code>\n\n<\/div>\n
    \n

    Arrow down and select <DiagnosticOn><\/code><\/p>\n\n

    \n\"arrow<\/span>... , \"enter<\/span>, \"enter<\/span>\n\n<\/div>\n
    r<\/span><\/span><\/span><\/span><\/span><\/span><\/span> and r<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span> will be displayed during regression calculations.<\/div>\n
    \n

    Access linear regression.<\/p>\n\n

    \n\"stat<\/span>\"arrow<\/span>\n\n<\/div>\n
    \n

    Select the form of y<\/em> = a<\/em> + bx<\/em>.<\/p>\n\n

    \n\"number<\/span>, \"enter<\/span>\n\n<\/div>\n<\/div>\n
    \nThe display will show:\n

    LinReg<\/span><\/p>\n\n

    \n
    y<\/em> = a<\/em> + bx<\/em><\/div>\n
    a<\/em> = \u20133176.909<\/div>\n
    b<\/em> = 1.617<\/div>\n
    r<\/em> = 2 0.924<\/div>\n
    r<\/em> = 0.961<\/div>\n<\/div>\n
    \nThis means the Line of Best Fit (Least Squares Line) is:\n
    \n
    y<\/em> = \u20133176.909 + 1.617x<\/em><\/div>\n
    Percent = \u20133176.909 + 1.617 (year #)<\/div>\n<\/div>\nThe correlation coefficient r<\/em> = 0.961\n

    To see the scatter plot:<\/span><\/p>\n\n

    \n
    \n

    Access graphing mode.<\/p>\n\n

    \n\"2nd<\/span>, [STAT PLOT]<\/code>\n\n<\/div>\n
    \n

    Select <1:plot 1><\/code> To access plotting - first graph.<\/p>\n\n

    \n\"enter<\/span>\n\n<\/div>\n
    \n

    Navigate and select <ON><\/code> to turn on Plot 1.<\/p>\n\n

    \n<ON><\/code> \"enter<\/span>\n\n<\/div>\n
    Navigate to the first picture.<\/div>\n
    \n

    Select the scatter plot.<\/p>\n\n

    \n\"enter<\/span>\n\n<\/div>\n
    Navigate to <Xlist><\/code>.<\/div>\n
    If [L1]<\/code> is not selected, press \"2nd<\/span>, [L1]<\/code> to select it.<\/div>\n
    \n

    Confirm that the data values are in [L1]<\/code>.<\/p>\n\n

    \n<ON><\/code> \"enter<\/span>\n\n<\/div>\n
    Navigate to <Ylist><\/code>.<\/div>\n
    \n

    Select that the frequencies are in [L2]<\/code>.<\/p>\n\n

    \n\"2nd<\/span>, [L2]<\/code> , \"enter<\/span>\n\n<\/div>\n
    \n

    Go back to access other graphs.<\/p>\n\n

    \n\"2nd<\/span>, [STAT PLOT]<\/code>\n\n<\/div>\n
    Use the arrows to turn off the remaining plots.<\/div>\n
    Access window mode to set the graph parameters.\n
    \n\"window<\/span>\n
    \n
    X<\/span>min<\/span><\/span><\/span>=<\/span>1970<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
    X<\/span>max<\/span><\/span><\/span>=<\/span>2000<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
    X<\/span>s<\/span>c<\/span>l<\/span><\/span><\/span>=<\/span>10<\/span><\/span><\/span><\/span><\/span><\/span><\/span> (spacing of tick marks on x<\/em>-axis)<\/div>\n
    Y<\/span>min<\/span><\/span><\/span>=<\/span>\u2212<\/span>0.05<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
    Y<\/span>max<\/span><\/span><\/span>=<\/span>60<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
    Y<\/span>s<\/span>c<\/span>l<\/span><\/span><\/span>=<\/span>10<\/span><\/span><\/span><\/span><\/span><\/span><\/span> (spacing of tick marks on y<\/em>-axis)<\/div>\n
    X<\/span>r<\/span>e<\/span>s<\/span><\/span><\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<\/div>\n<\/div>\n
    Be sure to deselect or clear all equations before graphing, using the instructions above.<\/div>\n
    Press the graph button to see the scatter plot. \"graph<\/span><\/div>\n<\/div>\n

    To see the regression graph:<\/span><\/p>\n\n

    \n
    \n

    Access the equation menu. The regression equation will be put into Y1.<\/p>\n\n

    \n\"Y=<\/span>\n\n<\/div>\n
    \n

    Access the vars menu and navigate to <5: Statistics><\/code>.<\/p>\n\n

    \n\"vars<\/span>, \"number<\/span>\n\n<\/div>\n
    Navigate to <EQ><\/code>.<\/div>\n
    \n

    <1: RegEQ><\/code> contains the regression equation which will be entered in Y1.<\/p>\n\n

    \n\"enter<\/span>\n\n<\/div>\n
    Press the graphing mode button. The regression line will be superimposed over the scatter plot.\n
    \n\"graph<\/span>\n\n<\/div>\n<\/div>\n

    To see the residuals and use them to calculate the critical point for an outlier:<\/span><\/p>\n\n

    \n
    \n

    Access the list. RESID will be an item on the menu. Navigate to it.<\/p>\n\n

    \n\"2nd<\/span>, [LIST]<\/code>, <RESID><\/code>\n\n<\/div>\n
    \n

    Confirm twice to view the list of residuals. Use the arrows to select them.<\/p>\n\n

    \n\"enter<\/span>, \"enter<\/span>\n\n<\/div>\n
    The critical point for an outlier is: 1.9<\/span>V<\/span><\/span>SSE<\/span><\/span>n<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> where:\n
    \n
    n<\/span><\/span><\/span><\/span><\/span><\/span><\/span> = number of pairs of data<\/div>\n
    SSE<\/span><\/span><\/span><\/span><\/span><\/span><\/span> = sum of the squared errors<\/div>\n
    \u2211<\/span><\/span>residual<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<\/div>\n<\/div>\n
    \n

    Store the residuals in [L3]<\/code>.<\/p>\n\n

    \n\"store<\/span>, \"2nd<\/span>, [L3]<\/code> , \"enter<\/span>\n\n<\/div>\n
    \n

    Calculate the (residual)<\/span><\/span>2<\/span><\/span>n<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>. Note that n<\/span><\/span>\u2212<\/span>2<\/span><\/span>=<\/span>8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n

    \n\"2nd<\/span>, [L3]<\/code> , \"x-squared<\/span>, \"division<\/span>, \"number<\/span>\n\n<\/div>\n
    \n

    Store this value in [L4]<\/code>.<\/p>\n\n

    \n\"store<\/span>, \"2nd<\/span>, [L4]<\/code> , \"enter<\/span>\n\n<\/div>\n
    \n

    Calculate the critical value using the equation above.<\/p>\n\n

    \n\"number<\/span>, \"decimal<\/span>, \"number<\/span>, \"multiplication<\/span>, \"2nd<\/span>, [V]<\/code> , \"2nd<\/span>, [LIST]<\/code> \"arrow<\/span>, \"arrow<\/span>, \"number<\/span>, \"2nd<\/span>, [L4]<\/code> , \"closing<\/span>, \"closing<\/span>, \"enter<\/span>\n\n<\/div>\n
    Verify that the calculator displays: 7.642669563. This is the critical value.<\/div>\n
    Compare the absolute value of each residual value in [L3]<\/code> to 7.64. If the absolute value is greater than 7.64, then the (x, y) corresponding point is an outlier. In this case, none of the points is an outlier.<\/div>\n<\/div>\n

    To obtain estimates of y<\/em> for various x<\/em>-values:<\/span>There are various ways to determine estimates for \"y.<\/em>\" One way is to substitute values for \"x<\/em>\" in the equation. Another way is to use the \"trace<\/span>on the graph of the regression line.<\/p>\n\n<\/section><\/section>

    TI-83, 83+, 84, 84+ instructions for distributions and tests<\/h1>\n

    Distributions<\/h2>\n

    Access DISTR<\/code> (for \"Distributions\").<\/p>\n

    For technical assistance, visit the Texas Instruments website at http:\/\/www.ti.com<\/a> and enter your calculator model into the \"search\" box.<\/p>\n

    Binomial Distribution<\/span><\/p>\n\n

    \n
    binompdf(n<\/em>,p<\/em>,x<\/em>)<\/code> corresponds to P<\/em>(X<\/em> = x<\/em>)<\/div>\n
    binomcdf(n<\/em>,p<\/em>,x<\/em>)<\/code> corresponds to P<\/em>(X \u2264 x)<\/div>\n
    To see a list of all probabilities for x<\/em>: 0, 1, . . . , n<\/em>, leave off the \"x<\/em><\/code>\" parameter.<\/div>\n<\/div>\n

    Poisson Distribution<\/span><\/p>\n\n

    \n
    poissonpdf(\u03bb,x<\/em>)<\/code> corresponds to P<\/em>(X<\/em> = x<\/em>)<\/div>\n
    poissoncdf(\u03bb,x<\/em>)<\/code> corresponds to P<\/em>(X<\/em> \u2264 x<\/em>)<\/div>\n<\/div>\n

    Continuous Distributions (general)<\/span><\/p>\n\n

    \n
    \u2212<\/span>\u221e<\/span><\/span><\/span><\/span><\/span><\/span><\/span> uses the value \u20131EE99 for left bound<\/div>\n
    \u221e<\/span><\/span><\/span><\/span><\/span><\/span><\/span> uses the value 1EE99 for right bound<\/div>\n<\/div>\n

    Normal Distribution<\/span><\/p>\n\n

    \n
    normalpdf(x<\/em>,\u03bc<\/em>,\u03c3<\/em>)<\/code> yields a probability density function value (only useful to plot the normal curve, in which case \"x<\/em><\/code>\" is the variable)<\/div>\n
    normalcdf(left bound, right bound, \u03bc<\/em>, \u03c3<\/em>)<\/code> corresponds to P<\/em>(left bound < X<\/em> < right bound)<\/div>\n
    normalcdf(left bound, right bound)<\/code> corresponds to P<\/em>(left bound < Z<\/em> < right bound) \u2013 standard normal<\/div>\n
    invNorm(p<\/em>,\u03bc<\/em>,\u03c3<\/em>)<\/code> yields the critical value, k<\/em>: P<\/em>(X<\/em> < k<\/em>) = p<\/em><\/div>\n
    invNorm(p<\/em>)<\/code> yields the critical value, k<\/em>: P<\/em>(Z<\/em> < k<\/em>) = p<\/em> for the standard normal<\/div>\n<\/div>\n

    Student's t<\/em>-Distribution<\/span><\/p>\n\n

    \n
    tpdf(x<\/em>,df<\/em>)<\/code> yields the probability density function value (only useful to plot the student-t<\/em>curve, in which case \"x<\/em><\/code>\" is the variable)<\/div>\n
    tcdf(left bound, right bound, df<\/em>)<\/code> corresponds to P<\/em>(left bound < t<\/em> < right bound)<\/div>\n<\/div>\n

    Chi-square Distribution<\/span><\/p>\n\n

    \n
    \u03a72<\/sup>pdf(x<\/em>,df<\/em>)<\/code> yields the probability density function value (only useful to plot the chi2<\/sup> curve, in which case \"x<\/em><\/code>\" is the variable)<\/div>\n
    \u03a72<\/sup>cdf(left bound, right bound, df<\/em>)<\/code> corresponds to P<\/em>(left bound < \u03a7<\/em>2<\/sup> < right bound)<\/div>\n<\/div>\n

    F Distribution<\/span><\/p>\n\n

    \n
    Fpdf(x<\/em>,dfnum<\/em>,dfdenom<\/em>)<\/code> yields the probability density function value (only useful to plot theF<\/em> curve, in which case \"x<\/em><\/code>\" is the variable)<\/div>\n
    Fcdf(left bound,right bound,dfnum<\/em>,dfdenom<\/em>)<\/code> corresponds to P<\/em>(left bound < F<\/em> < right bound)<\/div>\n<\/div>\n<\/section>

    Tests and Confidence Intervals<\/h2>\n

    Access STAT<\/code> and TESTS<\/code>.<\/p>\n

    For the confidence intervals and hypothesis tests, you may enter the data into the appropriate lists and press DATA<\/code> to have the calculator find the sample means and standard deviations. Or, you may enter the sample means and sample standard deviations directly by pressing STAT<\/code> once in the appropriate tests.<\/p>\n

    Confidence Intervals<\/span><\/p>\n\n

    \n
    ZInterval<\/code> is the confidence interval for mean when \u03c3 is known.<\/div>\n
    TInterval<\/code> is the confidence interval for mean when \u03c3 is unknown; s<\/em> estimates \u03c3.<\/div>\n
    1-PropZInt<\/code> is the confidence interval for proportion.<\/div>\n<\/div>\n
    NOTE<\/div>\n<\/header>

    The confidence levels should be given as percents (ex. enter \"95<\/code>\" or \".95<\/code>\" for a 95% confidence level).<\/p>\n\n<\/section><\/div>\n

    Hypothesis Tests<\/span><\/p>\n\n

    \n
    Z-Test<\/code> is the hypothesis test for single mean when \u03c3 is known.<\/div>\n
    T-Test<\/code> is the hypothesis test for single mean when \u03c3 is unknown; s<\/em> estimates \u03c3.<\/div>\n
    2-SampZTest<\/code> is the hypothesis test for two independent means when both \u03c3's are known.<\/div>\n
    2-SampTTest<\/code> is the hypothesis test for two independent means when both \u03c3's are unknown.<\/div>\n
    1-PropZTest<\/code> is the hypothesis test for single proportion.<\/div>\n
    2-PropZTest<\/code> is the hypothesis test for two proportions.<\/div>\n
    \u03a72<\/sup>-Test<\/code> is the hypothesis test for independence.<\/div>\n
    \u03a72<\/sup>GOF-Test<\/code> is the hypothesis test for goodness-of-fit (TI-84+ only).<\/div>\n
    LinRegTTEST<\/code> is the hypothesis test for Linear Regression (TI-84+ only).<\/div>\n<\/div>\n
    NOTE<\/div>\n<\/header>

    Input the null hypothesis value in the row below \"Inpt<\/code>.\" For a test of a single mean, \"\u03bc\u2205<\/code>\" represents the null hypothesis. For a test of a single proportion, \"p\u2205<\/code>\" represents the null hypothesis. Enter the alternate hypothesis on the bottom row.<\/p>\n\n<\/section><\/div>\n<\/section><\/section>","rendered":"

    \n

    Quick Tips<\/h1>\n

    Legend<\/span><\/p>\n

    \n
    \"A<\/span>represents a button press<\/div>\n
    [ ]<\/code> represents yellow command or green letter behind a key<\/div>\n
    < ><\/code> represents items on the screen<\/div>\n<\/div>\n

    To adjust the contrast<\/span>Press \"2nd<\/span>, then hold \"arrow<\/span>to increase the contrast or \"arrow<\/span>to decrease the contrast.<\/p>\n

    To capitalize letters and words<\/span>Press \"alpha<\/span>to get one capital letter, or press \"2nd<\/span>, then \"alpha<\/span>to set all button presses to capital letters. You can return to the top-level button values by pressing \"alpha<\/span>again.<\/p>\n

    To correct a mistake<\/span>If you hit a wrong button, just hit \"clear<\/span>and start again.<\/p>\n

    To write in scientific notation<\/span>Numbers in scientific notation are expressed on the TI-83, 83+, 84, and 84+ using E notation, such that…<\/p>\n

    \n
    4.321 E 4 = 4<\/span>.321<\/span>\u00d7<\/span>10<\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
    4.321 E \u20134 = 4<\/span>.321<\/span>\u00d7<\/span>10<\/span><\/span>\u20134<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<\/div>\n

    To transfer programs or equations from one calculator to another:<\/span>Both calculators:<\/strong> Insert your respective end of the link cable cable and press \"2nd<\/span>, then [LINK]<\/code>.<\/p>\n

    Calculator receiving information:<\/span><\/p>\n

    \n
    Use the arrows to navigate to and select <RECEIVE><\/code><\/div>\n
    Press \"enter<\/span>.<\/div>\n<\/div>\n

    Calculator sending information:<\/span><\/p>\n

    \n
    Press appropriate number or letter.<\/div>\n
    Use up and down arrows to access the appropriate item.<\/div>\n
    Press \"enter<\/span>to select item to transfer.<\/div>\n
    Press right arrow to navigate to and select <TRANSMIT><\/code>.<\/div>\n
    Press \"enter<\/span>.<\/div>\n<\/div>\n
    \n
    \n
    NOTE<\/div>\n<\/header>\n
    \n

    ERROR 35 LINK generally means that the cables have not been inserted far enough.<\/p>\n<\/section>\n<\/div>\n

    Both calculators:<\/strong> Insert your respective end of the link cable cable Both calculators: press \"2nd<\/span>, then [QUIT]<\/code> to exit when done.<\/p>\n<\/section>\n

    \n

    Manipulating One-Variable Statistics<\/h1>\n
    \n
    \n
    NOTE<\/div>\n<\/header>\n
    \n

    These directions are for entering data with the built-in statistical program.<\/p>\n<\/section>\n<\/div>\n\n\n\n\n\n\n\n\n\n
    Sample Data<\/span>We are manipulating one-variable statistics.<\/caption>\n
    Data<\/th>\nFrequency<\/th>\n<\/tr>\n<\/thead>\n
    \u20132<\/td>\n10<\/td>\n<\/tr>\n
    \u20131<\/td>\n3<\/td>\n<\/tr>\n
    0<\/td>\n4<\/td>\n<\/tr>\n
    1<\/td>\n5<\/td>\n<\/tr>\n
    3<\/td>\n8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    To begin:<\/span><\/p>\n

    \n
    \n

    Turn on the calculator.<\/p>\n

    \n\"on<\/span><\/p>\n<\/div>\n
    \n

    Access statistics mode.<\/p>\n

    \n\"stat<\/span><\/p>\n<\/div>\n
    \n

    Select <4:ClrList><\/code> to clear data from lists, if desired.<\/p>\n

    \n\"number<\/span>, \"enter<\/span><\/p>\n<\/div>\n
    \n

    Enter list [L1]<\/code> to be cleared.<\/p>\n

    \n\"2nd<\/span>, [L1]<\/code> , \"enter<\/span><\/p>\n<\/div>\n
    \n

    Display last instruction.<\/p>\n

    \n\"2nd<\/span>, [ENTRY]<\/code><\/p>\n<\/div>\n
    \n

    Continue clearing remaining lists in the same fashion, if desired.<\/p>\n

    \n\"arrow<\/span>, \"2nd<\/span>, [L2]<\/code> , \"enter<\/span><\/p>\n<\/div>\n
    \n

    Access statistics mode.<\/p>\n

    \n\"stat<\/span><\/p>\n<\/div>\n
    \n

    Select <1:Edit . . .><\/code><\/p>\n

    \n\"enter<\/span><\/p>\n<\/div>\n
    \n

    Enter data. Data values go into [L1]<\/code>. (You may need to arrow over to [L1]<\/code>).<\/p>\n

    \n
    \n

    Type in a data value and enter it. (For negative numbers, use the negate (-) key at the bottom of the keypad).<\/p>\n

    \n\"negative<\/span>, \"number<\/span>, \"enter<\/span><\/p>\n<\/div>\n
    Continue in the same manner until all data values are entered.<\/div>\n<\/div>\n<\/div>\n
    \n

    In [L2]<\/code>, enter the frequencies for each data value in [L1]<\/code>.<\/p>\n

    \n
    \n

    Type in a frequency and enter it. (If a data value appears only once, the frequency is “1”).<\/p>\n

    \n\"number<\/span>, \"enter<\/span><\/p>\n<\/div>\n
    Continue in the same manner until all data values are entered.<\/div>\n<\/div>\n<\/div>\n
    \n

    Access statistics mode.<\/p>\n

    \n\"stat<\/span><\/p>\n<\/div>\n
    Navigate to <CALC><\/code>.<\/div>\n
    \n

    Access <1:1-var Stats><\/code>.<\/p>\n

    \n\"enter<\/span><\/p>\n<\/div>\n
    \n

    Indicate that the data is in [L1]<\/code>…<\/p>\n

    \n\"2nd<\/span>, [L1]<\/code> , \"comma<\/span><\/p>\n<\/div>\n
    \n

    …and indicate that the frequencies are in [L2]<\/code>.<\/p>\n

    \n\"2nd<\/span>, [L2]<\/code> , \"enter<\/span><\/p>\n<\/div>\n
    The statistics should be displayed. You may arrow down to get remaining statistics. Repeat as necessary.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n
    \n

    Drawing Histograms<\/h1>\n
    \n
    \n
    NOTE<\/div>\n<\/header>\n
    \n

    We will assume that the data is already entered.<\/p>\n<\/section>\n<\/div>\n

    We will construct two histograms with the built-in STATPLOT application. The first way will use the default ZOOM. The second way will involve customizing a new graph.<\/p>\n

      \n
    1. \n

      Access graphing mode.<\/p>\n

      \n\"2nd<\/span>, [STAT PLOT]<\/code><\/div>\n<\/li>\n
    2. \n

      Select <1:plot 1><\/code> to access plotting – first graph.<\/p>\n

      \n\"enter<\/span><\/div>\n<\/li>\n
    3. \n

      Use the arrows navigate go to <ON><\/code> to turn on Plot 1.<\/p>\n

      \n<ON><\/code> , \"enter<\/span><\/div>\n<\/li>\n
    4. Use the arrows to go to the histogram picture and select the histogram. \"enter<\/span><\/li>\n
    5. Use the arrows to navigate to <Xlist><\/code>.<\/li>\n
    6. \n

      If “L1” is not selected, select it.<\/p>\n

      \n\"2nd<\/span>, [L1]<\/code> , \"enter<\/span><\/div>\n<\/li>\n
    7. Use the arrows to navigate to <Freq><\/code>.<\/li>\n
    8. \n

      Assign the frequencies to [L2]<\/code>.<\/p>\n

      \n\"2nd<\/span>, [L2]<\/code> , \"enter<\/span><\/div>\n<\/li>\n
    9. \n

      Go back to access other graphs.<\/p>\n

      \n\"2nd<\/span>, [STAT PLOT]<\/code><\/div>\n<\/li>\n
    10. Use the arrows to turn off the remaining plots.<\/li>\n
    11. Be sure to deselect or clear all equations before graphing.<\/strong><\/li>\n<\/ol>\n

      To deselect equations:<\/span><\/p>\n

      \n
      \n

      Access the list of equations.<\/p>\n

      \n\"Y=<\/span><\/p>\n<\/div>\n
      \n

      Select each equal sign (=).<\/p>\n

      \n\"arrow<\/span>\"arrow<\/span>\"enter<\/span><\/p>\n<\/div>\n
      Continue, until all equations are deselected.<\/div>\n<\/div>\n

      To clear equations:<\/span><\/p>\n

      \n
      \n

      Access the list of equations.<\/p>\n

      \n\"Y=<\/span><\/p>\n<\/div>\n
      \n

      Use the arrow keys to navigate to the right of each equal sign (=) and clear them.<\/p>\n

      \n\"arrow<\/span>\"arrow<\/span>\"clear<\/span><\/p>\n<\/div>\n
      Repeat until all equations are deleted.<\/div>\n<\/div>\n

      To draw default histogram:<\/span><\/p>\n

      \n
      \n

      Access the ZOOM menu.<\/p>\n

      \n\"ZOOM<\/span><\/p>\n<\/div>\n
      \n

      Select <9:ZoomStat><\/code>.<\/p>\n

      \n\"number<\/span><\/p>\n<\/div>\n
      The histogram will show with a window automatically set.<\/div>\n<\/div>\n

      To draw custom histogram:<\/span><\/p>\n

      \n
      Access window mode to set the graph parameters.<\/p>\n
      \n\"window<\/span><\/p>\n<\/div>\n
      \n
      \n
      X<\/span>min<\/span><\/span><\/span>=<\/span>\u20132.5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
      X<\/span>max<\/span><\/span><\/span>=<\/span>3.5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
      X<\/span>s<\/span>c<\/span>l<\/span><\/span><\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span> (width of bars)<\/div>\n
      Y<\/span>min<\/span><\/span><\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
      Y<\/span>max<\/span><\/span><\/span>=<\/span>10<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
      Y<\/span>s<\/span>c<\/span>l<\/span><\/span><\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span> (spacing of tick marks on y<\/em>-axis)<\/div>\n
      X<\/span>r<\/span>e<\/span>s<\/span><\/span><\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<\/div>\n<\/div>\n
      Access graphing mode to see the histogram.<\/p>\n
      \n\"graph<\/span><\/p>\n<\/div>\n<\/div>\n

      To draw box plots:<\/span><\/p>\n

      \n
      \n

      Access graphing mode.<\/p>\n

      \n\"2nd<\/span>, [STAT PLOT]<\/code><\/p>\n<\/div>\n
      \n

      Select <1:Plot 1><\/code> to access the first graph.<\/p>\n

      \n\"enter<\/span><\/p>\n<\/div>\n
      \n

      Use the arrows to select <ON><\/code> and turn on Plot 1.<\/p>\n

      \n\"enter<\/span><\/p>\n<\/div>\n
      \n

      Use the arrows to select the box plot picture and enable it.<\/p>\n

      \n\"enter<\/span><\/p>\n<\/div>\n
      Use the arrows to navigate to <Xlist><\/code>.<\/div>\n
      \n

      If “L1” is not selected, select it.<\/p>\n

      \n\"2nd<\/span>, [L1]<\/code> , \"enter<\/span><\/p>\n<\/div>\n
      Use the arrows to navigate to <Freq><\/code>.<\/div>\n
      \n

      Indicate that the frequencies are in [L2]<\/code>.<\/p>\n

      \n\"2nd<\/span>, [L2]<\/code> , \"enter<\/span><\/p>\n<\/div>\n
      \n

      Go back to access other graphs.<\/p>\n

      \n\"2nd<\/span>, [STAT PLOT]<\/code><\/p>\n<\/div>\n
      Be sure to deselect or clear all equations before graphing<\/strong> using the method mentioned above.<\/div>\n
      \n

      View the box plot.<\/p>\n

      \n\"graph<\/span>, [STAT PLOT]<\/code><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n
      \n

      Linear Regression<\/h1>\n
      \n

      Sample Data<\/h2>\n

      The following data is real. The percent of declared ethnic minority students at De Anza College for selected years from 1970\u20131995 was:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
      The independent variable is “Year,” while the independent variable is “Student Ethnic Minority Percent.”<\/caption>\n
      Year<\/th>\nStudent Ethnic Minority Percentage<\/th>\n<\/tr>\n<\/thead>\n
      1970<\/td>\n14.13<\/td>\n<\/tr>\n
      1973<\/td>\n12.27<\/td>\n<\/tr>\n
      1976<\/td>\n14.08<\/td>\n<\/tr>\n
      1979<\/td>\n18.16<\/td>\n<\/tr>\n
      1982<\/td>\n27.64<\/td>\n<\/tr>\n
      1983<\/td>\n28.72<\/td>\n<\/tr>\n
      1986<\/td>\n31.86<\/td>\n<\/tr>\n
      1989<\/td>\n33.14<\/td>\n<\/tr>\n
      1992<\/td>\n45.37<\/td>\n<\/tr>\n
      1995<\/td>\n53.1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
      \n
      Student Ethnic Minority Percentage<\/div>\n

      \"This<\/span>

      By hand, verify the scatterplot above.<\/figcaption><\/figure>\n
      \n
      \n
      NOTE<\/div>\n<\/header>\n
      \n

      The TI-83 has a built-in linear regression feature, which allows the data to be edited.The x<\/em>-values will be in [L1]<\/code>; the y<\/em>-values in [L2]<\/code>.<\/p>\n<\/section>\n<\/div>\n

      To enter data and do linear regression:<\/span><\/p>\n

      \n
      \n

      ON Turns calculator on.<\/p>\n

      \n\"on<\/span><\/p>\n<\/div>\n
      Before accessing this program, be sure to turn off all plots.<\/p>\n
      \n
      \n

      Access graphing mode.<\/p>\n

      \n\"2nd<\/span>, [STAT PLOT]<\/code><\/p>\n<\/div>\n
      \n

      Turn off all plots.<\/p>\n

      \n\"number<\/span>, \"enter<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n
      Round to three decimal places. To do so:<\/p>\n
      \n
      \n

      Access the mode menu.<\/p>\n

      \n\"mode<\/span>, [STAT PLOT]<\/code><\/p>\n<\/div>\n
      \n

      Navigate to <Float><\/code> and then to the right to <3><\/code>.<\/p>\n

      \n\"arrow<\/span>\"arrow<\/span><\/p>\n<\/div>\n
      \n

      All numbers will be rounded to three decimal places until changed.<\/p>\n

      \n\"enter<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n

      Enter statistics mode and clear lists [L1]<\/code> and [L2]<\/code>, as describe previously.<\/p>\n

      \n\"stat<\/span>, \"number<\/span><\/p>\n<\/div>\n
      \n

      Enter editing mode to insert values for x<\/em> and y<\/em>.<\/p>\n

      \n\"stat<\/span>, \"enter<\/span><\/p>\n<\/div>\n
      Enter each value. Press \"enter<\/span>to continue.<\/div>\n<\/div>\n

      To display the correlation coefficient:<\/span><\/p>\n

      \n
      \n

      Access the catalog.<\/p>\n

      \n\"2nd<\/span>, [CATALOG]<\/code><\/p>\n<\/div>\n
      \n

      Arrow down and select <DiagnosticOn><\/code><\/p>\n

      \n\"arrow<\/span>… , \"enter<\/span>, \"enter<\/span><\/p>\n<\/div>\n
      r<\/span><\/span><\/span><\/span><\/span><\/span><\/span> and r<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span> will be displayed during regression calculations.<\/div>\n
      \n

      Access linear regression.<\/p>\n

      \n\"stat<\/span>\"arrow<\/span><\/p>\n<\/div>\n
      \n

      Select the form of y<\/em> = a<\/em> + bx<\/em>.<\/p>\n

      \n\"number<\/span>, \"enter<\/span><\/p>\n<\/div>\n<\/div>\n
      \nThe display will show:<\/p>\n

      LinReg<\/span><\/p>\n

      \n
      y<\/em> = a<\/em> + bx<\/em><\/div>\n
      a<\/em> = \u20133176.909<\/div>\n
      b<\/em> = 1.617<\/div>\n
      r<\/em> = 2 0.924<\/div>\n
      r<\/em> = 0.961<\/div>\n<\/div>\n
      \nThis means the Line of Best Fit (Least Squares Line) is:<\/p>\n
      \n
      y<\/em> = \u20133176.909 + 1.617x<\/em><\/div>\n
      Percent = \u20133176.909 + 1.617 (year #)<\/div>\n<\/div>\n

      The correlation coefficient r<\/em> = 0.961<\/p>\n

      To see the scatter plot:<\/span><\/p>\n

      \n
      \n

      Access graphing mode.<\/p>\n

      \n\"2nd<\/span>, [STAT PLOT]<\/code><\/p>\n<\/div>\n
      \n

      Select <1:plot 1><\/code> To access plotting – first graph.<\/p>\n

      \n\"enter<\/span><\/p>\n<\/div>\n
      \n

      Navigate and select <ON><\/code> to turn on Plot 1.<\/p>\n

      \n<ON><\/code> \"enter<\/span><\/p>\n<\/div>\n
      Navigate to the first picture.<\/div>\n
      \n

      Select the scatter plot.<\/p>\n

      \n\"enter<\/span><\/p>\n<\/div>\n
      Navigate to <Xlist><\/code>.<\/div>\n
      If [L1]<\/code> is not selected, press \"2nd<\/span>, [L1]<\/code> to select it.<\/div>\n
      \n

      Confirm that the data values are in [L1]<\/code>.<\/p>\n

      \n<ON><\/code> \"enter<\/span><\/p>\n<\/div>\n
      Navigate to <Ylist><\/code>.<\/div>\n
      \n

      Select that the frequencies are in [L2]<\/code>.<\/p>\n

      \n\"2nd<\/span>, [L2]<\/code> , \"enter<\/span><\/p>\n<\/div>\n
      \n

      Go back to access other graphs.<\/p>\n

      \n\"2nd<\/span>, [STAT PLOT]<\/code><\/p>\n<\/div>\n
      Use the arrows to turn off the remaining plots.<\/div>\n
      Access window mode to set the graph parameters.<\/p>\n
      \n\"window<\/span><\/p>\n
      \n
      X<\/span>min<\/span><\/span><\/span>=<\/span>1970<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
      X<\/span>max<\/span><\/span><\/span>=<\/span>2000<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
      X<\/span>s<\/span>c<\/span>l<\/span><\/span><\/span>=<\/span>10<\/span><\/span><\/span><\/span><\/span><\/span><\/span> (spacing of tick marks on x<\/em>-axis)<\/div>\n
      Y<\/span>min<\/span><\/span><\/span>=<\/span>\u2212<\/span>0.05<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
      Y<\/span>max<\/span><\/span><\/span>=<\/span>60<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n
      Y<\/span>s<\/span>c<\/span>l<\/span><\/span><\/span>=<\/span>10<\/span><\/span><\/span><\/span><\/span><\/span><\/span> (spacing of tick marks on y<\/em>-axis)<\/div>\n
      X<\/span>r<\/span>e<\/span>s<\/span><\/span><\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<\/div>\n<\/div>\n
      Be sure to deselect or clear all equations before graphing, using the instructions above.<\/div>\n
      Press the graph button to see the scatter plot. \"graph<\/span><\/div>\n<\/div>\n

      To see the regression graph:<\/span><\/p>\n

      \n
      \n

      Access the equation menu. The regression equation will be put into Y1.<\/p>\n

      \n\"Y=<\/span><\/p>\n<\/div>\n
      \n

      Access the vars menu and navigate to <5: Statistics><\/code>.<\/p>\n

      \n\"vars<\/span>, \"number<\/span><\/p>\n<\/div>\n
      Navigate to <EQ><\/code>.<\/div>\n
      \n

      <1: RegEQ><\/code> contains the regression equation which will be entered in Y1.<\/p>\n

      \n\"enter<\/span><\/p>\n<\/div>\n
      Press the graphing mode button. The regression line will be superimposed over the scatter plot.<\/p>\n
      \n\"graph<\/span><\/p>\n<\/div>\n<\/div>\n

      To see the residuals and use them to calculate the critical point for an outlier:<\/span><\/p>\n

      \n
      \n

      Access the list. RESID will be an item on the menu. Navigate to it.<\/p>\n

      \n\"2nd<\/span>, [LIST]<\/code>, <RESID><\/code><\/p>\n<\/div>\n
      \n

      Confirm twice to view the list of residuals. Use the arrows to select them.<\/p>\n

      \n\"enter<\/span>, \"enter<\/span><\/p>\n<\/div>\n
      The critical point for an outlier is: 1.9<\/span>V<\/span><\/span>SSE<\/span><\/span>n<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> where:<\/p>\n

      n<\/span><\/span><\/span><\/span><\/span><\/span><\/span> = number of pairs of data<\/span><\/span><\/div>\n

      SSE<\/span><\/span><\/span><\/span><\/span><\/span><\/span> = sum of the squared errors<\/div>\n
      \u2211<\/span><\/span>residual<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<\/div>\n<\/div>\n
      \n

      Store the residuals in [L3]<\/code>.<\/p>\n

      \n\"store<\/span>, \"2nd<\/span>, [L3]<\/code> , \"enter<\/span><\/p>\n<\/div>\n
      \n

      Calculate the (residual)<\/span><\/span>2<\/span><\/span>n<\/span><\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>. Note that n<\/span><\/span>\u2212<\/span>2<\/span><\/span>=<\/span>8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \n\"2nd<\/span>, [L3]<\/code> , \"x-squared<\/span>, \"division<\/span>, \"number<\/span><\/p>\n<\/div>\n
      \n

      Store this value in [L4]<\/code>.<\/p>\n

      \n\"store<\/span>, \"2nd<\/span>, [L4]<\/code> , \"enter<\/span><\/p>\n<\/div>\n
      \n

      Calculate the critical value using the equation above.<\/p>\n

      \n\"number<\/span>, \"decimal<\/span>, \"number<\/span>, \"multiplication<\/span>, \"2nd<\/span>, [V]<\/code> , \"2nd<\/span>, [LIST]<\/code> \"arrow<\/span>, \"arrow<\/span>, \"number<\/span>, \"2nd<\/span>, [L4]<\/code> , \"closing<\/span>, \"closing<\/span>, \"enter<\/span><\/p>\n<\/div>\n
      Verify that the calculator displays: 7.642669563. This is the critical value.<\/div>\n
      Compare the absolute value of each residual value in [L3]<\/code> to 7.64. If the absolute value is greater than 7.64, then the (x, y) corresponding point is an outlier. In this case, none of the points is an outlier.<\/div>\n<\/div>\n

      To obtain estimates of y<\/em> for various x<\/em>-values:<\/span>There are various ways to determine estimates for “y.<\/em>” One way is to substitute values for “x<\/em>” in the equation. Another way is to use the \"trace<\/span>on the graph of the regression line.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/section>\n

      \n

      TI-83, 83+, 84, 84+ instructions for distributions and tests<\/h1>\n
      \n

      Distributions<\/h2>\n

      Access DISTR<\/code> (for “Distributions”).<\/p>\n

      For technical assistance, visit the Texas Instruments website at http:\/\/www.ti.com<\/a> and enter your calculator model into the “search” box.<\/p>\n

      Binomial Distribution<\/span><\/p>\n

      \n
      binompdf(n<\/em>,p<\/em>,x<\/em>)<\/code> corresponds to P<\/em>(X<\/em> = x<\/em>)<\/div>\n
      binomcdf(n<\/em>,p<\/em>,x<\/em>)<\/code> corresponds to P<\/em>(X \u2264 x)<\/div>\n
      To see a list of all probabilities for x<\/em>: 0, 1, . . . , n<\/em>, leave off the “x<\/em><\/code>” parameter.<\/div>\n<\/div>\n

      Poisson Distribution<\/span><\/p>\n

      \n
      poissonpdf(\u03bb,x<\/em>)<\/code> corresponds to P<\/em>(X<\/em> = x<\/em>)<\/div>\n
      poissoncdf(\u03bb,x<\/em>)<\/code> corresponds to P<\/em>(X<\/em> \u2264 x<\/em>)<\/div>\n<\/div>\n

      Continuous Distributions (general)<\/span><\/p>\n

      \n
      \u2212<\/span>\u221e<\/span><\/span><\/span><\/span><\/span><\/span><\/span> uses the value \u20131EE99 for left bound<\/div>\n
      \u221e<\/span><\/span><\/span><\/span><\/span><\/span><\/span> uses the value 1EE99 for right bound<\/div>\n<\/div>\n

      Normal Distribution<\/span><\/p>\n

      \n
      normalpdf(x<\/em>,\u03bc<\/em>,\u03c3<\/em>)<\/code> yields a probability density function value (only useful to plot the normal curve, in which case “x<\/em><\/code>” is the variable)<\/div>\n
      normalcdf(left bound, right bound, \u03bc<\/em>, \u03c3<\/em>)<\/code> corresponds to P<\/em>(left bound < X<\/em> < right bound)<\/div>\n
      normalcdf(left bound, right bound)<\/code> corresponds to P<\/em>(left bound < Z<\/em> < right bound) \u2013 standard normal<\/div>\n
      invNorm(p<\/em>,\u03bc<\/em>,\u03c3<\/em>)<\/code> yields the critical value, k<\/em>: P<\/em>(X<\/em> < k<\/em>) = p<\/em><\/div>\n
      invNorm(p<\/em>)<\/code> yields the critical value, k<\/em>: P<\/em>(Z<\/em> < k<\/em>) = p<\/em> for the standard normal<\/div>\n<\/div>\n

      Student’s t<\/em>-Distribution<\/span><\/p>\n

      \n
      tpdf(x<\/em>,df<\/em>)<\/code> yields the probability density function value (only useful to plot the student-t<\/em>curve, in which case “x<\/em><\/code>” is the variable)<\/div>\n
      tcdf(left bound, right bound, df<\/em>)<\/code> corresponds to P<\/em>(left bound < t<\/em> < right bound)<\/div>\n<\/div>\n

      Chi-square Distribution<\/span><\/p>\n

      \n
      \u03a72<\/sup>pdf(x<\/em>,df<\/em>)<\/code> yields the probability density function value (only useful to plot the chi2<\/sup> curve, in which case “x<\/em><\/code>” is the variable)<\/div>\n
      \u03a72<\/sup>cdf(left bound, right bound, df<\/em>)<\/code> corresponds to P<\/em>(left bound < \u03a7<\/em>2<\/sup> < right bound)<\/div>\n<\/div>\n

      F Distribution<\/span><\/p>\n

      \n
      Fpdf(x<\/em>,dfnum<\/em>,dfdenom<\/em>)<\/code> yields the probability density function value (only useful to plot theF<\/em> curve, in which case “x<\/em><\/code>” is the variable)<\/div>\n
      Fcdf(left bound,right bound,dfnum<\/em>,dfdenom<\/em>)<\/code> corresponds to P<\/em>(left bound < F<\/em> < right bound)<\/div>\n<\/div>\n<\/section>\n
      \n

      Tests and Confidence Intervals<\/h2>\n

      Access STAT<\/code> and TESTS<\/code>.<\/p>\n

      For the confidence intervals and hypothesis tests, you may enter the data into the appropriate lists and press DATA<\/code> to have the calculator find the sample means and standard deviations. Or, you may enter the sample means and sample standard deviations directly by pressing STAT<\/code> once in the appropriate tests.<\/p>\n

      Confidence Intervals<\/span><\/p>\n

      \n
      ZInterval<\/code> is the confidence interval for mean when \u03c3 is known.<\/div>\n
      TInterval<\/code> is the confidence interval for mean when \u03c3 is unknown; s<\/em> estimates \u03c3.<\/div>\n
      1-PropZInt<\/code> is the confidence interval for proportion.<\/div>\n<\/div>\n
      \n
      \n
      NOTE<\/div>\n<\/header>\n
      \n

      The confidence levels should be given as percents (ex. enter “95<\/code>” or “.95<\/code>” for a 95% confidence level).<\/p>\n<\/section>\n<\/div>\n

      Hypothesis Tests<\/span><\/p>\n

      \n
      Z-Test<\/code> is the hypothesis test for single mean when \u03c3 is known.<\/div>\n
      T-Test<\/code> is the hypothesis test for single mean when \u03c3 is unknown; s<\/em> estimates \u03c3.<\/div>\n
      2-SampZTest<\/code> is the hypothesis test for two independent means when both \u03c3’s are known.<\/div>\n
      2-SampTTest<\/code> is the hypothesis test for two independent means when both \u03c3’s are unknown.<\/div>\n
      1-PropZTest<\/code> is the hypothesis test for single proportion.<\/div>\n
      2-PropZTest<\/code> is the hypothesis test for two proportions.<\/div>\n
      \u03a72<\/sup>-Test<\/code> is the hypothesis test for independence.<\/div>\n
      \u03a72<\/sup>GOF-Test<\/code> is the hypothesis test for goodness-of-fit (TI-84+ only).<\/div>\n
      LinRegTTEST<\/code> is the hypothesis test for Linear Regression (TI-84+ only).<\/div>\n<\/div>\n
      \n
      \n
      NOTE<\/div>\n<\/header>\n
      \n

      Input the null hypothesis value in the row below “Inpt<\/code>.” For a test of a single mean, “\u03bc\u2205<\/code>” represents the null hypothesis. For a test of a single proportion, “p\u2205<\/code>” represents the null hypothesis. Enter the alternate hypothesis on the bottom row.<\/p>\n<\/section>\n<\/div>\n<\/section>\n<\/section>\n\n\t\t\t

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