stat

Q1

A random variable X is normally distributed with a mean of ten and a standard deviation of five. A sample of size n=4 was taken from this population.

a. (1 pt) What is the probability that the sample mean is greater than twelve?

b. (1 pt) Would your ability to answer the question change if you were told that X is not normally distributed? Why?

Q2

										Table A
										How Typical Students Spend Their Time
										Daily Activities	Hypothesized Hours	Known standard deviation	Sample mean (n=50)
										Sleeping	8.7	2	7.8
										Leisure and Sports	4.1	0.5	4.2
										Educational Activities	3.3	3	2.4
										Working	2.4	2	2.9
										Other	2.3	0.7	3.1
										Traveling	1.4	0.2	1.4
										Eating and Drinking	1	0.7	1.2
										Grooming	0.8	0.3	1
										Total	24		24
h. An upper-tail test for the average hours spent grooming (use α=0.05)

The data in Table A describes time use for an average weekday for full- time college students. The first column provides various types of activities, the second column provides the hypothesized number of hours a typical student spends on each activity (taken from the website of the American Bureau of Labor Statistics), and the third column provides the population standard deviation (σ) for each activity. To test whether these data are reflective of student time use at your school, you selected a sample of 50 of your classmates and asked them to provide data on their time use for an average weekday. The sample means you calculated for each activity are provided in the fourth column. Using the information provided in Table A, find the p-value for each of the tests posed in questions a.-h., using the provided value of α to draw your conclusion of whether or not to reject the null hypothesis.

a. (1 pt) A two-tail test for the average number of sleep hours (use α=0.1)

b. (1 pt) An upper-tail test for the average hours spent on leisure and sports (use α=0.1)

c. (1 pt) A lower-tail test for the average hours spent on educational activities (use α=0.05)

d. (1 pt) A two-tail test for the average hours spent working (use α=0.01)

e. (1 pt) An upper-tail test for the average hours spent on other activities (use α=0.01)

f. (1 pt) A two-tail test for the average hours spent traveling (use α=0.05)

g. (1 pt) An upper-tail test for the average hours spent eating and drinking (use α=0.05)

h. (1 pt) An upper-tail test for the average hours spent grooming (use α=0.05)

Q3

(2 pt) The United States government claims DUI arrests average 22,096 per state per year. A sample of size n=10 states finds the mean to be 44,002. If DUI arrests are normally distributed with a standard deviation of 28,584, can it be concluded at the 1% significance level that DUI arrests are higher than the government claims?

Q4

Joe wants to know if he receives the same number of emails as his co- workers, who claim to get seventeen emails daily with a known population standard deviation of five emails. He takes a random sample of twenty days and records how many emails he receives. His sample average is 17.9 emails per day.

a. (1 pt) Construct a 95% interval for the mean number of daily emails.

b. (1 pt) Can Joe conclude at the 5% significance level that he gets the same number of emails per day as claimed by his co-workers?