Answer
No, see explanations.
Work Step by Step
Given $n1=200, X1=49, \hat p1=49/200=0.245, n2=200, X2=62, \hat p2=62/200=0.31$
a. State the hypotheses and identify the claim.
$H_o: p1=p2$
$H_a: p1\ne p2$ (claim, two tail test)
b. Find the critical value(s
$\alpha/2=0.025, |z_c|=2.81$
c. Compute the test value.
$\bar p=\frac{49+62}{200+200}=0.2775, \bar q=1-\bar p=0.7225,$
$z=\frac{0.245-0.31-0}{\sqrt {0.2775\times0.7225\times(1/200+1/200)}}=-1.45$
d. Make the decision.
As $z>-2.81$, we do not reject the null hypothesis.
e. Summarize the results.
At the 0.05 level of significance, there is not sufficient evidence to conclude a difference in proportions.
