Question

in a previous year, 54% of women aged 15 and older lived alone. a sociologist tests whether the 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 α = 0.05 level of significance to conclude the proportion has changed? in 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. h₀: p = 0.54 versus h₁: p ≠ 0.54 (type integers or decimals. do not round.) find the test statistic for this hypothesis test. z₀ = 0.49 (round to two decimal places as needed.) determine the p - value for this hypothesis test. p - value = 0.624 (round to three decimal places as needed.) state the conclusion for this hypothesis test. since the p - value is than α, h₀. there sufficient evidence at the α = level of significance to conclude that the proportion of women aged 15 and older who are living alone has changed (type an integer or a decimal. do not round.)

Explanation:

Step1: Compare P - value and significance level

We are given \(\alpha = 0.05\) and \(P - value=0.624\).

Step2: Make a decision

Since \(0.624>0.05\) (i.e., \(P - value>\alpha\)), we fail to reject the null hypothesis \(H_0\).

Answer:

Since the \(P -\)value is greater than \(\alpha\), fail to reject \(H_0\). There is not sufficient evidence at the \(\alpha = 0.05\) level of significance to conclude that the proportion of women aged 15 and older who are living alone has changed.