13C Coreq

In the next preview assignment and in the next class, you will need to be able to rewrite  equations and inequalities, use formulas to make inferences about two means, and  calculate a difference between two measurements.

Screen Time Across America 

In 2018, Apple released a program that tracks screen time usage on their phones. In  order to have a good idea of how much time Americans spend on their phones, a study  was conducted with 2,103 participants. The dataset we are going to look at for this  corequisite support activity contains the mean daily data usage for Apple users in each  of the 50 states across America.[1] To read more about this study, go to https://simpletexting.com/screen-time-survey/.

Go to the DCMP Describing and Exploring Quantitative Variables tool at  https://dcmathpathways.shinyapps.io/EDA_quantitative/.

Next, locate “Enter Data” on the drop-down menu and select “Your Own.” For “Name of Variable,” type in “Average Daily Screen Time (in minutes)” and then copy and paste  the following daily screen time data (continued on the following page) in the “Enter  Observations” box.

State Average Daily  Screen Time  

(in minutes)

 State Average Daily  Screen Time  (in minutes)
Alabama 170 Montana 154
Alaska 134 Nebraska 182
Arizona 276 Nevada 262
Arkansas 145 New Hampshire 135
California 204 New Jersey 182
Colorado 166 New Mexico 177
Connecticut 262 New York 206
Delaware 166 North Carolina 205
Florida 213 North Dakota 192
Georgia 198 Ohio 231
Hawaii 133 Oklahoma 131
Idaho 161 Oregon 132
Illinois 220 Pennsylvania 213
Indiana 220 Rhode Island 165
Iowa 163 South Carolina 155
Kansas 146 South Dakota 154
Kentucky 149 Tennessee 196
Louisiana 144 Texas 186
Maine 165 Utah 155
Maryland 199 Vermont 124
Massachusetts 195 Virginia 179
Michigan 188 Washington 173
Minnesota 140 West Virginia 150
Mississippi 146 Wisconsin 211
Missouri 211 Wyoming 134

Question 1

1) What is the mean you calculated using the data analysis tool?

Question 2

2) What does the mean represent in this context?

Question 3

3) We are going to see how far above and below the mean the average daily screen  time (in minutes) is for some states. In order to find this difference, use the following  formula:

Difference = (average daily screen time, in minutes) – (mean)

For example, for Alabama, we would take the average daily screen time (170) and  subtract the mean (178): 170 – 178 = –8

a) Find the difference between Oregon and the mean.

b) Describe what this difference represents in this context.

c) Find the difference between Michigan and the mean.

d) Describe what this difference represents in this context.

Question 4

4) If you live in a different state than the two above, find the difference between the  state you live in and the mean. Describe what the difference represents in this  context.

Question 5

5) Consider the equation [latex]a=b[/latex]. You can rewrite this equation in an equivalent form that has 0 on the right side by subtracting [latex]b[/latex] from both sides, as follows:

[latex]a=b[/latex]

[latex]a-b=b-b[/latex]

[latex]a-b=0[/latex]

a) Consider the equation [latex]\mu_{1}=\mu_{2}[/latex]. Rewrite this equation in an equivalent form that has 0 on the right side by subtracting [latex]\mu_{2}[/latex] from both sides.

b) Consider the inequality [latex]\mu_{1}<\mu_{2}[/latex]. Rewrite this inequality in an equivalent form that has 0 on the right side by subtracting [latex]\mu_{2}[/latex] from both sides. c) Consider the inequality [latex]\mu_{1}>\mu_{2}[/latex]. Rewrite this inequality in an equivalent form that has 0 on the right side by subtracting [latex]\mu_{2}[/latex] from both sides.

Question 6

6) Provide plausible values for the population mean that would make the following statements true.

a) [latex]\mu_{1}-\mu_{2}=0[/latex]

b) [latex]\mu_{1}-\mu_{2}<0[/latex] c) [latex]\mu_{1}-\mu_{2}>0[/latex]

Question 7

7) The formula for the test statistic to compare two population means contains multiple  values for the sample mean, sample standard deviation, sample size, and population  mean. To prepare for the preview assignment and in-class activity, match each symbol in the following table with its description by drawing lines between them.

Symbol Description
[latex]s_{1}[/latex] difference between the population means
[latex]n_{1}[/latex] population mean of Group 1
[latex]\bar{x}_{2}[/latex] sample standard deviation of Group 1
[latex]\mu_{2}[/latex] sample size of Group 1
[latex]\mu_{1}-\mu_{2}[/latex] sample mean of Group 2
[latex]s_{2}[/latex] difference between the sample means
[latex]n_{2}[/latex] sample mean of Group 1
[latex]\mu_{1}[/latex] population mean of Group 2
[latex]\bar{x}_{1}-\bar{x}_{2}[/latex] sample size of Group 2
[latex]\bar{x}_{1}[/latex] sample standard deviation of Group 2
  1. Wilkinson, D. (n.d.). Screen time trends in the age of COVID-19. SimpleTexting.  https://simpletexting.com/screentime-smartphone-usage-statistics/ ↵