Question

in a previous year, 54% of women aged 15 and older lived alone. a sociologist tests whether this percentage is different today by conducting a random sample of 600 women aged 15 and older and finds that 330 are living alone. is there sufficient evidence at the \\( \alpha = 0.05 \\) level of significance to conclude the proportion has changed?

determine whether all of requirements for the hypothesis test are satisfied. complete the following sentence

because \\( n p _ { 0 } ( 1 - p _ { 0 } ) = 149.0 > 10 \\), the sample size is less than 5% of the population size, and the sample is a random sample, all of the requirements for testing the hypothesis are satisfied

(round to one decimal place as needed)

identify the null and alternative hypotheses for this test

\\( h _ { 0 } \\) versus \\( h _ { 1 } \\)

(type integers or decimals. do not round)

Explanation:

Step1: Determine the null hypothesis

The null hypothesis \(H_0\) is a statement of no change. Here, the proportion \(p\) is equal to the previous proportion. So \(H_0:p = 0.54\)

Step2: Determine the alternative hypothesis

The alternative hypothesis \(H_1\) is a statement that the proportion has changed. So \(H_1:p
eq0.54\)

Answer:

\(H_0:p = 0.54\) versus \(H_1:p
eq0.54\)