Question

Over the past several years, the proportion of one-person households has been increasing. The Census Bureau would like to test the hypothesis that the proportion of one-person households exceeds 0.27. A random sample of 125 households found that 43 consisted of one person. The Census Bureau would like to set α = 0.05. Use the critical value approach to test this hypothesis. Explain.

Answer 1

d

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.27
Alternative Hypothesis, Ha: p > 0.27

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.344 - 0.27)/sqrt(0.27*(1-0.27)/125)
z = 1.86

reject the null hypothesis.