Statistics Technology Lab
karlakay456
Math2150LProject3-2.docxMath 2150L – Statistics Technology Lab – Project #3 NAME __________________________________
ASSIGNED: Monday October 26, 2020 DUE: Monday November 2, 2020
Provide answers to the questions that follow by inserting your answers within each part of each problem. If you choose to include graphs, you can copy-and-paste the graph inside of the question. If you are copying and pasting R output, please include only relevant R output, not all R output.
PROBLEM 1 – Watching More TV? (50 points)
A sociologist claims that children ages 6–17 spent more time watching television in 1981 than children 6–17 do today. A study was conducted in 1981 to find the time that children age 6–17 spent watching television on weekdays. The results (in hours per weekday) are shown below.
|
2.0 |
2.5 |
2.1 |
2.3 |
2.1 |
1.6 |
2.6 |
2.1 |
2.1 |
2.4 |
|
2.1 |
2.1 |
1.5 |
1.7 |
2.1 |
2.3 |
2.5 |
3.3 |
2.2 |
2.9 |
|
1.5 |
1.9 |
2.4 |
2.2 |
1.2 |
3.0 |
1.0 |
2.1 |
1.9 |
2.2 |
Recently, a similar study was conducted. The results are shown below.
|
2.9 |
1.8 |
0.9 |
1.6 |
2.0 |
1.7 |
2.5 |
1.1 |
1.6 |
2.0 |
|
1.4 |
1.7 |
1.7 |
1.9 |
1.6 |
1.7 |
1.2 |
2.0 |
2.6 |
1.6 |
|
1.5 |
2.5 |
1.6 |
2.1 |
1.7 |
1.8 |
1.1 |
1.4 |
1.2 |
2.3 |
Do these data provide sufficient evidence that children ages 6–17 spent more time watching television in 1981 than children 6–17 do today? Use = 0.05.
a. (5 pts) Is it safe to assume that the two random samples are approximately symmetric? Justify.
b. (5 pts) State the hypotheses being tested.
c. (5 pts) Write the R commands for data entry, feel free to use suspension point notation. Be sure to use the same variable names for all questions that follow so that it is not necessary to include any additional data entry R commands.
d. (10 pts) Provide only the relevant R command(s) used to generate the p-value of the hypothesis test.
e. (5 pts) Report the statistical decision concerning Ho and numerical information used to obtain this decision.
f. (10 pts) State the non-statistical conclusion in the context of this problem.
g. (10 pts) Report and interpret an appropriate confidence interval. Is your interpretation of the confidence interval consistent with the conclusion reached in part f? Explain.
PROBLEM 2 – Spending More Time Sleeping? (50 points)
A sociologist claims that children ages 12–14 spent less time sleeping in 1981 than children 12–14 do today. A study was conducted in 1981 to find the time that children age 12–14 spent sleeping on weekdays. The results (in hours per weekday) are shown below.
|
7.3 |
7.5 |
7.7 |
7.8 |
6.9 |
7.9 |
8.3 |
7.9 |
8 |
8.3 |
Recently, a similar study was conducted. The results are shown below.
|
9.2 |
9.1 |
10 |
9.3 |
9.6 |
8 |
9.5 |
8.2 |
9 |
8.6 |
Do these data provide sufficient evidence that children ages 12–14 spent less time sleeping in 1981 than children 6–17 do today? Use = 0.05.
a. (5 pts) Is it safe to assume that the two random samples are approximately symmetric? Justify.
b. (5 pts) State the hypotheses being tested.
c. (5 pts) Write the R commands for data entry, feel free to use suspension point notation. Be sure to use the same variable names for all questions that follow so that it is not necessary to include any additional data entry R commands.
d. (10 pts) Provide only the relevant R command(s) used to generate the p-value of the hypothesis test.
e. (5 pts) Report the statistical decision concerning Ho and numerical information used to obtain this decision.
f. (10 pts) State the non-statistical conclusion in the context of this problem.
g. (10 pts) Report and interpret an appropriate confidence interval. Is your interpretation of the confidence interval consistent with the conclusion reached in part f? Explain.
