Question

Given two independent random samples with the following results:

Given two independent random samples with the following results: ni = 586 n2 = 404 x = 161 X2 = 68 Can it be concluded that there is a difference between the two population proportions? Use a significance level of a= 0.05 for the test. Copy Data Step 1 of 6: State the null and alternative hypotheses for the test. Answer 2 Points Keypad Ho: P1 HAPI P2 - P2

Answer 1

1)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

2)
p1cap = X1/N1 = 161/586 = 0.275
p1cap = X2/N2 = 68/404 = 0.168

3)
pcap = (X1 + X2)/(N1 + N2) = (161+68)/(586+404) = 0.231

4)
Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.275-0.168)/sqrt(0.231*(1-0.231)*(1/586 + 1/404))
z = 3.93

5)
Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

6)
Reject Null hypothesis