The average number of prescriptions filled at a pharmacy per person in the United States in 2019 was 11.6. An Illinois health official wants to test whether or not the mean number of prescriptions per capita in Illinois is different than 11.6. They randomly sample 104 Illinois residents and compute a sample mean of 10.9 prescriptions per person. Assume that the population standard deviation is known to be= 3.2 prescriptions per person. The official will conduct the test at a 5% significance level.

a. State hypotheses to be tested.

b. Is this test right-tailed, left-tailed or two tailed?

c. Compute test statistic (z-value).

d. Compute P-value

e. What does the P-value represent?

f. Based on the 5% significance level, what decision should the official make?

g. Does the decision change at a 1% significance level? Explain.