Question

Conduct the following test at the α = 0.05 level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume that the samples were obtained independently using simple random sampling. Test whether p1≠p2. Sample data are x1=30​, n1=254​, x2=36​, and n2=302.

​(a) Determine the null and alternative hypotheses. Choose the correct answer below.

A.

H0: p1=0 versus H1: p1=0

B.

H0: p1=p2 versus H1: p1<p2

C.

H0: p1=p2 versus H1: p1>p2

D.

H0: p1=p2 versus H1: p1≠p2

​(b) The test statistic

z0 is __?__.

​(Round to two decimal places as​ needed.)

​(c) The​ P-value is

__?__.

​(Round to three decimal places as​ needed.)

Test the null hypothesis. Choose the correct conclusion below.

A.

Do not reject the null hypothesis because there is not sufficient evidence to conclude that p1≠p2.

B.

Do not reject the null hypothesis because there is sufficient evidence to conclude that p1>p2.

C.

Reject the null hypothesis because there is not sufficient evidence to conclude that p1<p2.

D.

Reject the null hypothesis because there is sufficient evidence to conclude that p1≠p2.

Answer 1

Answer)

Null hypothesis Ho : P1=P2

Alternate hypothesis Ha : P1 is not equal to P2

Test statistics z = (p1-p2)/standard error

Standard error = √p*(1-p) * √{(1/n1)+(1/n2)}

P1 = 30/254

P2 = 36/302

N1 = 254

N2 = 302

P = combined proportion = (30+36)/(254+302)

Test statistics z = -0.04

From z table, p(z<-0.04) = 0.4840

But our test is two tailed

So, p-value is = 2*0.484 = 0.968

As the obtained p-value is greater than the given significance level of 0.05

Do not reject the null hypothesis, because there is not sufficient evidence to conclude that p1 is not equal to p2