There are 8 problems in this homework. Please write down your name and student ID, and show your work clearly and in details. For each problem of hypothesis testing, make sure to clearly state your Null and Alternative hypotheses along with all supporting calculations and you conclusion.

1. A random sample of 45 classrooms in a certain state had a sample mean of 22 students per classroom with a standard deviation of 6. Is there reason to believe that the average number of students per classroom in this state is greater than 20? Use .05 level of significance. Also compute the p-value for this test.

2. A car manufacture believes that a certain type of tire in their product line has a mean life greater than or equal to 35. You have reason to doubt this claim and select a random sample of 13 of these tires, which were found to have an average life of 33.7 months with a standard deviation of 3.2 months. Does this test give evidence that the true mean is less than 35? Use .01 level of significance. Also approximate the p-value with a range of values.

3. A pollster believes that 65% of all people in a certain city age 18-25 will voted for the democratic candidate in the presidential election this year. To test this claim a random sample of 280 registered voters was taken, and 165 indicated that they would vote for the democratic candidate. Test at the .01 level of significance. Also compute the p-value for this test.

4. A large public library claims that its average visitor spends 30 minutes using the internet. A sociologist believes this claim is incorrect. The sociologist plans to conduct a test at the .10 level of significance by collecting a random sample of 64 library visitors. The standard deviation of the sample is 16. If, in reality, the true population mean is 25 minutes, what is the probability that the test will commit a type II error? Also, find the power of the test.

5. Suppose we sample 55 items from a population whose standard deviation is 3, and test at the .05 significance level, the claim that the population mean is greater than 25. Find the probability of committing a type II error if, in reality, the population mean is 27. Also, find the power of the test.

6. A student claims that 20% of MU students plan to attend our football bowl game. Another student believes that the actual percentage is less than that. To prove his point, the second student surveyed 400 MU students and conducted a test at the .05 level of significance. Find the probability of committing a type II error if, in reality, the true proportion is .15. Also, find the power of the test.

7. To compare the salaries of two firms, A and B, two independent random samples of employees were taken. The following represents the findings (in thousands).

Company	1	2	3	4	5	6	7	8	9	10
A	41.5	39	47	102	89	62.5	55	50	48	62
B	38	90	80	62	55	60	61	71

At the .01 significance level, determine whether there is a mean difference between the salaries A and B. (Assume that the two population variances are equal.)

8. Suppose that independent random samples of appraised value of homes in two Missouri counties were collected and produced the following (in thousands):

Compute a 90% confidence Interval for the mean difference of appraised value of homes in the two counties.

County	Sample size	Sample Mean	Sample Standard Dev.
Boone	31	200	30
Cooper	33	150	40

Compute a 90% confidence Interval for the mean difference of appraised value of homes in the two counties.