Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions p 1p1 and p 2p2 at the given level of significance alphaα using the given sample statistics. Assume the sample statistics are from independent random samples. Claim: p 1p1equals=p 2p2, alphaαequals=0.100.10 Sample statistics: x 1x1equals=5959, n 1n1equals=171171 and x 2x2equals=3636, n 2n2equals=203203 Can a normal sampling distribution be used? No Yes

Identify the null and alternative hypotheses.

Null Hypothesis, :    or   

Alternate Hypothesis, :  or    

Yes, normal sampling distribution can be used.

Step-by-step explanation:

We are given that the sample statistics are from independent random samples. Claim: = , alpha(α) = 0.10 Sample statistics: =59, =171 and =36, = 203

We have to test the claim about the difference between two population proportions and at the given level of significance alpha(α) using the given sample statistics.

Let = population proportion of first group

      = population proportion of second group

SO, Null Hypothesis, :    or   

Alternate Hypothesis, :  or    

The test statistics that will be used here is Two-sample z proportion statistics;

              T.S. =  ~ N(0,1)

where, = = sample proportion of first group

            = = sample proportion of second group

              = sample size of first group = 171

              = sample size of second group = 203

So, Yes here normal sampling distribution can be used because the proportion test is approximately followed by a normal z distribution.