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# Chi square test and regression analysis

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1. A researcher selects a random sample of college students and measures the number of hours they spend watching television per week and their grade point average. The results are as follows:

X Y
Subject # TV hours GPA
1 50 1.90
2 20 2.20
3 19 2.40
4 10 3.30
5 9 2.90
6 14 2.50
7 7 3.50
8 40 1.95
9 30 2.00
10 4 3.90

a. Calculate the descriptive statistics for both variables.
b. Construct a scatter plot using TV Hours as the X-axis and GPA as the Y-axis. Include the regression line and the regression equation. What percent of the change in GPA is predicted by the change in the TV hours?
c. What is the predicted GPA if a person watches 15 hours of television per week?

2. A researcher is interested in whether social assertiveness might be influenced by training procedures. Two groups of college sophomores are randomly selected. Group A subjects are assigned to the "training sessions" and group B subjects do not receive the training. Both groups are given a "Social Assertiveness" test (higher scores indicate greater assertiveness). The results are the following:

Group A: 14, 11, 10, 10, 8, 6, 8, 9, 10, 11, 12

Group B: 12, 10, 10, 8, 7, 3, 8, 6, 5, 4, 6, 7, 9

a. Construct a 90% confidence interval for each group.

b. Perform the appropriate statistical test to determine if there is a statistical difference between the two groups at the 0.05 level.

3. A researcher is interested in demonstrating that ingestion of the drug magnesium permoline (MgPe) increases retention of learned material. A group of 16 subjects is randomly selected from WSSU students. The subjects are then randomly assigned to one of four conditions: A receives placebo, B receives 10cc of MgPe, C receives 20 CC of MgPe, and D receives 30 cc of MgPe. All subjects are then given some material to read and four hours later are tested for retention (high scores indicate high retention).

A B C D
8 10 11 10
6 7 6 8
6 8 8 7
5 9 12 11
6 11 14 10
5 7 13 11
7 9 11 10
3 6 9 9

a. Identify the independent and dependent variables.
b. Do the appropriate statistical test.
c. Do you accept or reject the null hypothesis?
d. Show what conditions are equal and what conditions are different.
e. What conclusions can you draw from this study?

4. One possible side effect of air pollution is genetic damage. A study designed to examine this problem exposed one group of mice air near a steel mill and another group to air in a rural area. The study compared the number of Hm-2 gene mutations in each group. The data table is below.

_____________Location____________
Mutation Steel Mill Air Rural Air
_______________________________________________________________
Yes 30 25

No___________________70____________________125________________________

a. State the null hypothesis.
b. Calculate the chi-square statistic.
c. Calculate the p-value from Table F.
d. At the 5% level, is there evidence to conclude that location and mutation are related?