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. lias the proportion of adults who totally abstain from alcohol changed? Use the Alpha=0.10 level of significance. Determine the null and alternative hypotheses. Choose the correct answer below. H0: P1 = 0 versusH1: p1 0 H0: P1 =p2 versus H1: p1 p2 H0: p1=p2 versus H1: p1>p2 H0: p,=p2 versus H1: p1

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]