Question

in october 1947, the gallup organization surveyed 1100 adults and asked, are you a total abstainer from, or do you on occasion consume, alcoholic beverages? of the 1100 adults surveyed, 407 indicated that they were total abstainers. in a portion of the results of a recent survey, the same question was asked of 800 adults and 240 indicated that they were total abstainers. complete parts (a) and (b).
interpret the p - value.
if the population proportions are equal, one would expect a sample difference proportion greater than the absolute value of the one observed in about 1 out of 1000 repetitions of this experiment. (round to the nearest integer as needed.)
state the conclusion for this hypothesis test.
○ a. do not reject ( h_0 ). there is not sufficient evidence at the ( alpha = 0.05 ) level of significance to suggest the proportion of adults who totally abstain from alcohol has changed.
○ b. reject ( h_0 ). there is sufficient evidence at the ( alpha = 0.05 ) level of significance to suggest the proportion of adults who totally abstain from alcohol has changed.
○ c. reject ( h_0 ). there is not sufficient evidence at the ( alpha = 0.05 ) level of significance to suggest the proportion of adults who totally abstain from alcohol has changed.
○ d. do not reject ( h_0 ). there is sufficient evidence at the ( alpha = 0.05 ) level of significance to suggest the proportion of adults who totally abstain from alcohol has changed.

Explanation:

Step1: Understand the hypothesis test decision rule

In hypothesis testing, if the P - value is less than the significance level ($\alpha$), we reject the null hypothesis ($H_0$). Here, $\alpha = 0.05$. The P - value interpretation given is that if population proportions are equal, a sample difference proportion greater than the absolute value of the observed one occurs about 1 out of 1000 times. This implies a very small P - value (since 1/1000=0.001 < 0.05).

Step2: Apply the decision rule

Since the P - value (0.001) < $\alpha$ (0.05), we reject the null hypothesis. Rejecting $H_0$ means there is sufficient evidence to suggest a change.

Answer:

B. Reject \(H_{0}\). There is sufficient evidence at the \(\alpha = 0.05\) level of significance to suggest the proportion of adults who totally abstain from alcohol has changed.