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Part I:
1) Suppose a candidate running for sheriff claims that she will reduce the average speed of emergency response
to less than 30 minutes (30 mins. is thought to be the average response time with the current sheriff). There
are no pas records, so the actual standard deviation of such response times cannot be determined. Thanks
to this campaign, she is elected sheriff, and careful records are now kept. The response times for the first month are:
26, 30, 28, 29, 25, 28, 32, 35, 24, 23 (times are in mins.)
Using an alpha level of 0.05 did the sheriff keep her promise? (show all 5 steps of hypothesis testing, explain your
conclusion).
2) A study was done of personality characteristics of 100 students who were tested at the beginning and end of their first
year of college. The researchers reported the results in the following table:
Personality Scale | Fall | Spring | Difference |
M | SD | M | SD | M | SD |
Anxiety | 16.82 | 4.21 | 15.32 | 3.84 | 1.50 | 1.85 |
Depression | 89.32 | 8.39 | 86.24 | 8.91 | 3.08 | 4.23 |
Introversion | 59.89 | 6.87 | 60.12 | 7.11 | 0.23 | 2.22 |
Neuroticism | 38.11 | 5.39 | 37.32 | 6.02 | 0.89 | 4.21 |
For each of the 4 personality scales, perform a t-test to determine whether there was a difference between
Fall and Spring (use an alpha level of 0.05, and assume 2-tailed tests). State all of your hypotheses and conclusions.
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