12. A researcher would like to determine whether a new tax on cigarettes has had any effect on peoples behavior. During the year before the tax was imposed, stores located in rest areas on the state thruway reported selling an average of = 410 packs per day with = 60. The distribution of daily sales was approximately normal.

For a sample of n = 16 days following the new tax, the researcher found an average of M = 386 packs per day for the same stores.

a. What is the value of test statistic that you calculate?

(2 point)

b. What is the critical value of Z with a two tailed test at .05?

(2 point)

c. Is the sample mean sufficient to conclude that there was a significant change in cigarette

purchases after the new tax, using a two-tailed test with = .05? Say why yes or why no.

(2 point)

d. If the population standard deviation was = 20, is the result sufficient to conclude that

there is a significant difference? Show how the calculations are different here.

(2 point)

e. Explain why the two tests lead to different outcomes. Explain what this says about the SD and hypothesis testing.

(2 point)