Question

Conduct a 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 the samples were obtained independently from a large population using simple random sampling. Test whether p1>p2. The sample data are x1=125, n1=243,x2=139, and n2=307.

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

A. H0: p1=p2 versus H1: p1>p2

B. H0: p1=0 versus H1: p1≠0

C. H0: p1=p2 Versus H1: p1

D.H0: p1=p2 versus H1: p1≠p2

(b) the test​ statistic?

(c) the​ P-value?

Answer 1

To Test :-

A. H0: p1=p2 versus H1: p1>p2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 125 + 139 ) / ( 243 + 307 )
= 0.48

Z = 1.44

Test Criteria :-
Reject null hypothesis if

= 1.44 < 1.64, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z > 1.44 )
P value = 0.0749
Reject null hypothesis if P value <
Since P value = 0.0749 > 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 at 5% level of significance.