STAT 200 PSU Quiz 8 STAT 200 PSU Quiz 8.docx

1.

A shoe company wants to compare two materials, A and B, for use on the soles of boys' shoes. In this example, each of ten boys in a study wore a special pair of shoes with the sole of one shoe made from Material A and the sole on the other shoe made from Material B. The sole types were randomly assigned to account for systematic differences in wear between the left and right foot. After three months, the shoes are measured for wear. Let Ho: μ_d = 0 versus Ha: μ_d ≠ 0. From this random sample of 10 boys, the sample mean difference was 0.41 and S_d was 0.387.

What is the value of the test statistic?

[removed]A) t = 0.00 
[removed]B) t = 3.18 
[removed]C) t = 3.35 
[removed]D) t = 4.74 

Feedback: First, recognize that this is a paired t-test. Then the t test statistic is 3.35 and is found by taking the sample mean difference minus the hypothesized value then dividing by the standard error (not standard deviation!). This, then, is (0.41 - 0)/(0.387/sq.rt. 10) or 0.41/0.122 = 3.35

2.

A shoe company wants to compare two materials, A and B, for use on the soles of boys' shoes. In this example, each of ten boys in a study wore a special pair of shoes with the sole of one shoe made from Material A and the sole on the other shoe made from Material B. The sole types were randomly assigned to account for systematic differences in wear between the left and right foot. After three months, the shoes are measured for wear. Let Ho: μ_d = 0 versus Ha: μ_d ≠ 0. From this random sample of 10 boys, the sample mean difference was 0.41 and S_d was 0.387.

If the p-value for this test is 0.009, then for a significance level of alpha = 0.05, are the results statistically significant?

[removed]A) No, results are not statistically significant because the p-value < 0.05. 
[removed]B) Yes, results are statistically significant because the p-value < 0.05. 
[removed]C) No, results are not statistically significant because the p-value > 0.05 
[removed]D) Yes, results are statistically significant because the p-value > 0.05. 

Feedback: Yes, results are statistically significant because the p-value < 0.05.