{"id":301,"date":"2021-07-14T15:59:10","date_gmt":"2021-07-14T15:59:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/section-exercises-4\/"},"modified":"2023-12-05T09:44:11","modified_gmt":"2023-12-05T09:44:11","slug":"section-exercises-4","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/section-exercises-4\/","title":{"raw":"Section Exercises","rendered":"Section Exercises"},"content":{"raw":"

Facts About the Chi-Square Distribution - Practice<\/h2>\r\n
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\r\n\r\n1. If the number of degrees of freedom for a chi-square distribution is 25, what is the population mean and standard deviation?\r\n\r\n<\/div>\r\n
2. If df<\/em> > 90, the distribution is _____________. If df<\/em> = 15, the distribution is ________________.<\/div>\r\n<\/section><\/div>\r\n
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3. When does the chi-square curve approximate a normal distribution?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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4. Where is \u03bc<\/em> located on a chi-square curve?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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5. Is it more likely the df<\/em> is 90, 20, or two in the graph?<\/p>\r\n\r\n

\"This<\/span><\/figure>\r\n<\/div>\r\n
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Goodness-of-Fit Test - Practice<\/h2>\r\nDetermine the appropriate test to be used in the next three exercises.<\/em>\r\n
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\r\n\r\n6. An archeologist is calculating the distribution of the frequency of the number of artifacts she finds in a dig site. Based on previous digs, the archeologist creates an expected distribution broken down by grid sections in the dig site. Once the site has been fully excavated, she compares the actual number of artifacts found in each grid section to see if her expectation was accurate.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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7. An economist is deriving a model to predict outcomes in the stock market. He creates a list of expected points on the stock market index for the next two weeks. At the close of each day\u2019s trading, he records the actual points on the index. He wants to see how well his model matched what actually happened.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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\r\n\r\n8. A personal trainer is putting together a weight-lifting program for her clients. For a 90-day program, she expects each client to lift a specific maximum weight each week. As she goes along, she records the actual maximum weights her clients lifted. She wants to know how well her expectations met with what was observed.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\nUse the following information to answer the next five exercises:<\/em> A teacher predicts what the distribution of grades on the final exam will be and they are recorded in the table.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Grade<\/th>\r\nProportion<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
A<\/td>\r\n0.25<\/td>\r\n<\/tr>\r\n
B<\/td>\r\n0.30<\/td>\r\n<\/tr>\r\n
C<\/td>\r\n0.35<\/td>\r\n<\/tr>\r\n
D<\/td>\r\n0.10<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

The actual distribution for a class of 20 is in the table below.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Grade<\/th>\r\nFrequency<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
A<\/td>\r\n7<\/td>\r\n<\/tr>\r\n
B<\/td>\r\n7<\/td>\r\n<\/tr>\r\n
C<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
D<\/td>\r\n1<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
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9. d<\/span>f<\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span> ______<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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10. State the null and alternative hypotheses.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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\r\n\r\n11. \u03c72<\/sup><\/em> test statistic = ______\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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\r\n\r\n12. p<\/em>-value = ______\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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\r\n\r\n13. At the 5% significance level, what can you conclude?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\nUse the following information to answer the next nine exercises:<\/em> The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in the table below.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Ethnicity<\/th>\r\nNumber of Cases<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
White<\/td>\r\n2,229<\/td>\r\n<\/tr>\r\n
Hispanic<\/td>\r\n1,157<\/td>\r\n<\/tr>\r\n
Black\/African-American<\/td>\r\n457<\/td>\r\n<\/tr>\r\n
Asian, Pacific Islander<\/td>\r\n232<\/td>\r\n<\/tr>\r\n
<\/td>\r\nTotal = 4,075<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe percentage of each ethnic group in Santa Clara County is as in the table below.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Ethnicity<\/th>\r\nPercentage of total county population<\/th>\r\nNumber expected (round to two decimal places)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
White<\/td>\r\n42.9%<\/td>\r\n1748.18<\/td>\r\n<\/tr>\r\n
Hispanic<\/td>\r\n26.7%<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Black\/African-American<\/td>\r\n2.6%<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Asian, Pacific Islander<\/td>\r\n27.8%<\/td>\r\n<\/td>\r\n<\/tr>\r\n
<\/td>\r\nTotal = 100%<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
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\r\n\r\n14. If the ethnicities of AIDS victims followed the ethnicities of the total county population, fill in the expected number of cases per ethnic group.\u00a0Perform a goodness-of-fit test to determine whether the occurrence of AIDS cases follows the ethnicities of the general population of Santa Clara County.<\/em>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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\r\n\r\n15. H0<\/sub><\/em>: _______\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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\r\n\r\n16. Ha<\/sub><\/em>: _______\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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17. Is this a right-tailed, left-tailed, or two-tailed test?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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\r\n\r\n18. degrees of freedom = _______\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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19. \u03c72<\/sup><\/em> test statistic = _______<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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20. p<\/em>-value = _______<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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21. Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade in the region corresponding to the p<\/em>-value.<\/p>\r\n\r\n

\"This<\/span><\/figure>\r\n

Let \u03b1<\/em> = 0.05<\/p>\r\n\r\n

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  1. Decision: ________________<\/li>\r\n \t
  2. Reason for the Decision: ________________<\/li>\r\n \t
  3. Conclusion (write out in complete sentences): ________________<\/li>\r\n<\/ol>\r\n<\/div>\r\n
    <\/div>\r\n<\/section><\/div>\r\n
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    22. Does it appear that the pattern of AIDS cases in Santa Clara County corresponds to the distribution of ethnic groups in this county? Why or why not?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section>\r\n

    Test of Independence - Practice<\/h2>\r\n

    Determine the appropriate test to be used in the next three exercises.<\/em><\/p>\r\n\r\n

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    \r\n\r\n23. A pharmaceutical company is interested in the relationship between age and presentation of symptoms for a common viral infection. A random sample is taken of 500 people with the infection across different age groups.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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    \r\n\r\n24. The owner of a baseball team is interested in the relationship between player salaries and the team winning percentage. He takes a random sample of 100 players from different organizations.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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    \r\n\r\n25. A marathon runner is interested in the relationship between the brand of shoes runners wear and their run times. She takes a random sample of 50 runners and records their run times as well as the brand of shoes they were wearing.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\nUse the following information to answer the next seven exercises:<\/em> Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken. The table below\u00a0shows the results. The railroad wants to know if a passenger\u2019s choice in ticket class is independent of the distance they must travel.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Traveling Distance<\/th>\r\nThird class<\/th>\r\nSecond class<\/th>\r\nFirst class<\/th>\r\nTotal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    1\u2013100 miles<\/td>\r\n21<\/td>\r\n14<\/td>\r\n6<\/td>\r\n41<\/td>\r\n<\/tr>\r\n
    101\u2013200 miles<\/td>\r\n18<\/td>\r\n16<\/td>\r\n8<\/td>\r\n42<\/td>\r\n<\/tr>\r\n
    201\u2013300 miles<\/td>\r\n16<\/td>\r\n17<\/td>\r\n15<\/td>\r\n48<\/td>\r\n<\/tr>\r\n
    301\u2013400 miles<\/td>\r\n12<\/td>\r\n14<\/td>\r\n21<\/td>\r\n47<\/td>\r\n<\/tr>\r\n
    401\u2013500 miles<\/td>\r\n6<\/td>\r\n6<\/td>\r\n10<\/td>\r\n22<\/td>\r\n<\/tr>\r\n
    Total<\/td>\r\n73<\/td>\r\n67<\/td>\r\n60<\/td>\r\n200<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
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    \r\n\r\n26. State the hypotheses.\r\n