Higher Taxes survey - Hypothesis Testing

Show all work. State H0 and H1 where appropriate. (Use a 95% confidence level unless another level is specified.) Answers must be with reasons

Exhibit T1: According to a 1992 survey, a 40% of the American population would support higher taxes to pay for health insurance. A state government is considering offering a health insurance plan and took a survey of 400 residents and found that 50% would support higher taxes. Use this result to test the results of the 1992 survey apply in the state. use a 99% confidence level.

a) State the null and alternative hypothesis in each case and find a critical value of each case.

What is the 'reject' region? Compute a test ratio and find a p-value for the hypothesis in each case.

(i) The state government wants to test that the fraction of people who favored higher taxes for health insurance is below the proportion of interest.
(ii) The state government wants to test that the fraction of people who favored higher taxes for health insurance is above the proportion of interest.
(iii) The state government wants to test that the fraction of people who favored higher taxes for health insurance is equal to the proportion of interest.

B) Find the power of the test if the tru proportion is 50% and:
(i) The alternate hypothesis is that the fraction of people is above the proportion of interest.
(ii) The alternate hypothesis is that the fraction of people does not equal the proportion of interest.

C) Assuming that the proportion of interest is correct, is the sample size given above adequate to find the true proportion within .005 (1/2 of 1%)? (Don't say yes or no without calculating the size that you actually need.)

D) If the alternate hypothesis is that the fraction of people is above the proportion of interest, create an appropriate interval for the hypothesis test.