You are hired by the mayor of California to study whether a tax on liquor has de
ID: 3061677 • Letter: Y
Question
You are hired by the mayor of California to study whether a
tax on liquor has decreased the share of California residents who report to
abuse of alcohol. You are able to obtain, for a sample of 9822 individuals,
information about their alcohol consumption habits.
N=9822
Abuse alcohol before tax a sample of 974
Abuse alcohol after tax a sample of 958
A. Using the data in alcohol data calculate the t statistic for test-
ing H0 against H1.
B. Obtain the p-value for the test (because of the large sample size, just
use the standard normal distribution tabulated in Table G.1.)
C. Explain what is the meaning of the p-value.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1 = P2
Alternative hypothesis: P1 P2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.09835
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.00425
z = (p1 - p2) / SE
z = 0.38
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 0.38 or greater than 0.38.
Thus, the P-value = 0.704
Interpret results. Since the P-value (0.704) is greater than the significance level (0.05), we have to accept the null hypothesis.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.