A local church parish wants to raise money to add to their campus. In a sample f

Question

A local church parish wants to raise money to add to their campus. In a sample from a previous fund raising campaign, the parish found that of the 140 people in the sample they contacted, that 65 actually contributed money. Of those that contributed money, the average contribution was $826 with a standard deviation of $267. In the recent fundraising campaign, a sample of 92 people revealed that 52 have contributed money with an average contribution of $1,197 and a standard deviation of $397. When testing (at the 5% level of significance) whether the proportion of peole who are contributing has increased, what is the test statistic? (please round your answer to 2 decimal places) and show your work please... :)

Explanation / Answer

Formulating the hypotheses          
Ho: p1 - p2   >=   0  
Ha: p1 - p2   <   0  
Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 = 65/140 =   0.464285714      
p2 = x2/n2 = 52/92 =   0.565217391      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.066691553      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -1.513410215 = -1.51 [ANSWER]

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Hi! In case they want the absolute value, you can also answer z = 1.51. [ALTERNATE ANSWER]      

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