Question

Of men aged 65 and over 20.5% are still in the US labor force. A random sample of 120 retired male teachers indicated that 38 were still working. Test the claim that the proportion is greater than 20.5% at 0.10.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.205
Alternative Hypothesis, Ha: p > 0.205

Rejection Region
This is right tailed test, for α = 0.1
Critical value of z is 1.28.
Hence reject H0 if z > 1.28

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.3167 - 0.205)/sqrt(0.205*(1-0.205)/120)
z = 3.03

P-value Approach
P-value = 0.0012
As P-value < 0.1, reject the null hypothesis.