Question

question 12 AND 13 please

Question 12 Commute times in the U.S. are heavily skewed to the right. We select a Type numbers in the boxes random sample of 210 people from the 2000 U.S. Census who reported a non- 10 points zero commute time. In this sample the mean commute time is 28.1 minutes with a standard deviation of 18.8 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance. What is the p-value for this hypothesis test? Your answer should be rounded to 4 decimal places. Question 13 Dean Halverson recently read that full-time college students study 20 hours Type numbers in the boxes each week. She decides to do a study at her university to see if there is 10 points evidence that students study an average of more than 20 hours each week. A random sample of 31 students were asked to keep a diary of their activities over a period of several weeks. It was found that the average number of hours that the 31 students studied each week was 22.4 hours. The sample standard deviation of 3-7 hours. Find the p-value. The p-value should be rounded to 4-decimal places,

Answer 1

Ane (12) Given, sample size, n=210 Sample mean, na 28-1 Sample standard Deviation, s= 18.8. claim is to test whether mean is less than half-an-hour - Bonduites) Hoi Ma 30 minutes I ho =30 Hair liz 30 minutes Given Rest 20.05. for 2 € 0.05 we get to = 1.6 Consider t statute ta ă-ho - 28-1-30 a-1-465 slon 18-8/1210 ^ t = -1.465 de for t= 1.465 Ip-value we get = 0.9247 / - 1 p-value = 0.9277 30.05 at, to is not rejected

13 Givery Sample size, n=31 and sample mean, n = 22-4 Sample standard deviation, s= 3.7 Here consider Claim to test whether mean is more than 20 how Hele Hoir ho > 20 Hal- les < 20 de Here to = 20 now consider 22.4-20 3.612 test statistie te 3-7/ for t = 3-612 t=3-612 we get, p-value = 0.9995