Question

Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her university to see if there is evidence that students study an average of less than 20 hours each week. A random sample of 32 students were asked to keep a diary of their activities over a period of several weeks. It was found that he average number of hours that the 32 students studied each week was 19.1 hours. The sample standard deviation of 4.2 hours. Find the p -value.

the p -value should be rounded to 4-decimal places.

A criminal investigator conducts a study on the accuracy of fingerprint matching and recruits a random sample of 35 people to participate. Since this is a random sample of people, we don’t expect the fingerprints to match the comparison print. In the general population, a score of 80 indicates no match. Scores greater than 80 indicate a match. If the mean score suggests a match, then the fingerprint matching criteria are not accurate.

The null hypothesis is that the mean match score is 80. The alternative hypothesis is that the mean match score is greater than 80.

The criminal investigator chooses a 5% level of significance. She performs the experiment and analyzes the results. She uses a t-test for a mean and obtains a p-value of 0.04.

Which of the following is a reasonable interpretation of her results?

1. This suggests that there is evidence that the mean match score is greater than 80. This suggests that the fingerprint matching criteria are not accurate.
2. If there is a treatment effect, the sample size was too small to detect it. This suggests that we need a larger sample to determine if the fingerprint matching criteria are not accurate.
3. She cannot reject the null hypothesis. This suggests that the fingerprint matching criteria could be accurate.
4. This suggests that there is evidence that the mean match score is equal to 80. This suggests that the fingerprint matching criteria is accurate.

Answer 1

Page No. Date Page No. Given ur. 20. n-32, ore 219.1, s=4.2 Ho u =20 Vis hier al 20 under Hog Test statistic is t = -el gol-20 sisn 4.21532 = P-value. Pltnrs 2 t) p(tzi < -1.21) - 0.0119 I s n. 35 Hor ur so vis Hi M280 az 540.05 P-value = 0.04 P-value La Reject Mull Hypothais. This suggest that the there is endance that the mean score is greater than 80. This suggest that the finger print matching criteria are not accurate.