Question

Conduct the following test at the alphaαequals=0.050.05 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=28​, n1=255​, x2=36​, and n2=301.

Answer 1

To Test :-

H0 :- P1 = P2

H1 :- p1≠p2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 28 + 36 ) / ( 255 + 301 )
= 0.1151

Z = -0.36

Test Criteria :-
Reject null hypothesis if

= -0.36 > -1.96, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( Z < -0.36 )
P value = 0.7188
Reject null hypothesis if P value <
Since P value = 0.7188 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that  p1≠p2.