Question

Given two independent random samples with the following results:

n1=350 n2=475

p1=0.55 p2=0.68

Can it be concluded that the proportion found in Population 2 exceeds the proportion found in Population 1? Use a significance level of α=0.05 for the test. Step 1 of 5 : State the null and alternative hypotheses for the test.

State the null and alternative hypotheses for the test

Find the values of the two sample proportions, pˆ1 and pˆ2. Round to 3 decimal places

Compute the weighted estimate of p, p‾. Round to 3 decimal places

Compute the value of the test statistic. Round to 2 decimal places

Determine the decision rule for rejecting the null hypothesis H_0. Round to 3 decimal places [ (Reject H₀ if (t or absolute value of t) is (< or >)   (value) ]

Make a decision to reject or fail to reject the null hypothesis.

Answer 1

To Test :-

H0 :- P1 = P2

H1 :- P1 < P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 192.5 + 323 ) / ( 350 + 475 )
= 0.6248

Z = -3.81

Test Criteria :-
Reject null hypothesis if

= -3.81 < -1.64, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z < -3.81 )
P value = 0.0001
Reject null hypothesis if P value <
Since P value = 0.0001 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that the proportion found in Population 2 exceeds the proportion found in Population 1.