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. To conduct the hypothesis test, what distribution would you use to calculate the critical value and the p-value?

a. the Student's t-distribution with 124 degrees of freedom
b. the Student's t-distribution with 125 degrees of freedom
c. the standard normal distribution
d. the Student's t-distribution with 42 degrees of freedom

Answer 1

a. the Student's t-distribution with 124 degrees of freedom

Explanation:

We have no information about the standard deviation of the population, just for the sample, which means that the student's t-distribution is used.

Degrees of freedom

Sample size subtracted by 1.

125 households were sampled.

125 - 1 = 124 degrees of freedom.

So the correct answer is:

a. the Student's t-distribution with 124 degrees of freedom