Statistics

Homework 7

1. Dr. Johnson is interested in the relationship between thoughtfulness and risk-taking behavior. A sample of her data is below. Test whether or not there is a correlation between these two variables using alpha = .05, two-tailed / non-directional.

Risk-taking
Subject Thoughtfulness Behavior
1 0 5
2 1 4
3 2 5
4 2 2
5 3 3
6 3 4
7 4 3
8 5 1

a. What are the null & alternative hypotheses? (1 pt)
b. What are the degrees of freedom and critical value? (1/2 pt)
c. Calculate the Pearson correlation (6 pts)
d. Reject or fail to reject the null? What conclusions can be made based on this correlation? (2 pts)

Compute the regression equation for the data from question #1. Using the regression equation, compute the risk-taking behavior predicted score for someone who scores a 3 on thoughtfulness (4 pts).
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Brand A Brand B Brand C
5 14 11

2. A sample of 30 people tastes three brands of instant coffee and each identifies his/her preference. Test if there is a preference in brand using a Chi Square goodness of fit test. Alpha = .05.
a. What are the null and alternative hypotheses (1pt)?
b. What are the degrees of freedom and critical value (1/2pt)?
c. Calculate the statistic (3pts).
d. Reject or fail to reject the null? What conclusions can be made about brand preference (be specific if you reject) (1pt)?

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3. A statistics instructor would like to know if it is worthwhile to require students to do homework assignments. For one section of the statistics course, homework is assigned. For another section, the same problems are suggested but not required as homework. At the end of the semester, all students take the final exam. The grade distribution is shown below. Do these data indicate a significant difference between the grade distributions for students with homework versus students with no homework? Test with a chi square test for independence using alpha of .05.
a. What are the null and alternative hypotheses? (1 pt)
b. What are the degrees of freedom and the critical value? (1/2 pt)
c. Calculate the chi square (6 pts)
d. Reject or fail to reject the null? What conclusions can be made about HW assignments (be specific)? (1 pt)
Grade
A B C D F
HW 12 15 17 5 1
No HW 12 21 28 25 14