An organization surveyed 1100 adults and asked Are you a tot

An organization surveyed 1,100 adults and asked, \"Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?\" Of the 1,100 adults surveyed, 362 indicated that they were total abstainers. Sixty years later, the same question was asked of 1,100 adults and 435 indicated that they were total abstainers. Has the proportion of adults who totally abstain from alcohol changed? Use the a = 0.05 level of significance. Determine the null and alternative hypotheses. Choose the correct answer below. a- H0: Pi =p2 versus H1:p1p2 The test statistic z0 is Q. (Round to two decimal places as needed.) The P-value is Q. (Round to three decimal places as needed.) What is the result of this hypothesis test? Do not reject the null hypothesis because there is not sufficient evidence to conclude that the proportion of adults who totally abstain from alcohol has changed at the a = 0.05 level of significance. Do not reject the null hypothesis because there is sufficient evidence to conclude that the proportion of adults who totally abstain from alcohol has changed at the a = 0.05 level of significance. Reject the null hypothesis because there is sufficient evidence to conclude that the proportion of adults who totally abstain from alcohol has changed at the a = 0.05 level of significance. Reject the null hypothesis because there is not sufficient evidence to conclude that the proportion of adults who totally abstain from alcohol has changed at the a = 0.05 level of significance.

Solution

a)

Formulating the hypotheses          
Ho: p1 = p2
Ha: p1 =/= p2 [ANSWER, C]

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b)

Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.329090909      
p2 = x2/n2 =    0.395454545      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.02044639      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -3.245738627 = -3.25 [ANSWER]

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c)      
          
          
Also, the p value is, as this is two tailed (I didn\'t round off z here)          
          
P =    0.001171463   [ANSWER]

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d)  
          
As P < 0.05,

OPTION C: REJECT THE NULL HYPOTHESIS, THERE IS SUFFICIENT EVIDENCE... [ANSWER]