Question

Suppose you are a statistics consultant, hired to study whether a tax on alcohol has decreased average alcohol consumption in Australia. For a given sample of randomly selected individuals, you are able to obtain the difference in alcohol consumption (in litres) for the years before and after the tax. For person i, who is randomly sampled from the population, Yi denotes the change in alcohol consumption. Suppose that your sample size is n = 900 and you obtain the sample mean y = −0.97 and sample standard deviation s = 13.8. a. State the null and alternative hypotheses and explain the type of test you will conduct. [ 2 marks ] b. Conduct the test of the above hypotheses. [ 5 marks ] c. What is the P value of the test statistic? Interpret the P value? [ 2 marks ] d. What has been implicitly assumed in your analysis about other determinants of alcohol consumption over the two-year period in order to infer causality from the tax change to alcohol consumption? [

Answer 1

a. Here the null and alternative hypotheses are:

H0: Y = 0 against H1: Y 0.

Here we will go for paired t test, since we have the data for

pairwise difference and we have to check the significance

of the difference in values.

b. The test-statistic is, T = , where, y = sample mean of

difference = - 0.97, s = 13.8, n = 900

Thus, T = - 2.1087.

Under H0, T ~ t-distribution with (n-1) i.e. 899 d.f.

The critical value is = [Assuming 5% level of

significance] = 1.963.

Since, observed test-statistic > critical value, we reject the

null hypothesis.

c. The p-value = 2 P(T < - 2.1087) = 0.0176. (Ans).

d. We assume the observations considered in the sample

are independent of each other. (Ans).