Two different simple random samples are drawn from two diffe

Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 15 having a common attribute. The second sample consists of 1800 people with 1301 of them having the same common attribute. Compare the results from a hypothesis test of p 1p1=p 2p2 with a 0.01 significancelevel and a 99% confidence interval estimate of p 1p1p 2p2.

Identify the test statistic. _________ (Round to two decimal places as needed.)

Solution

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 =    0.5      
p2 = x2/n2 =    0.722777778      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.091894777      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -2.424270292 = -2.42 [ANSWER]