Question

This Question: pts Question Help In a previous year, 01% of females aged 15 years of age and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 300 females aged 15 years of age and older and finds that 195 are living alone. Is there sufficient evidence at the 0.01 level of significance to conclude the proportion has changed? Identify the null and alternative hypotheses for this test. O A. Ho p=0.61 Hp > 0.61 OD HD 0.61 H:p0.61 OB. Ho p > 0.61 Hip=0.61 OE. HOD=0.61 Hp0.61 OCHOP-061 Hp<0.61 OF. Hop<0.61 Hp0.61 Find the test statistic for this hypothesis test -(Round to two decimal places as needed.) Determine the P-value for this hypothesis test. P-value - (Round to three decimal places as needed.) State the conclusion for this hypothesis test. O A Reject Ho. There is sufficient evidence at the a=0.01 level of significance to conclude that the proportion of females who are living alone has changed. OB. Reject Ho. There is not sufficient evidence at the 0.01 level of significance to conclude that the proportion of females who are living alone has changed. O c. Do not reject Ho. There is sufficient evidence at the c 0.01 level of significance to conclude that the proportion of females who are living alone has changed. OD. Do not reject Ho. There is not sufficient evidence at the cr=0.01 level of significance to conclude that the proportion offer who are living alone has changed. lick to select your answer(s).

Answer 1

HO: p=0.61 H1 :p #0.61 Population proportion = po = 0.61 Sample number of events = x =195 Sample size = n =300 Sample proportion = p = 195/300 = 0.65 The test statistic is, 2= p - PO Po (1 - Po) (0.65-0.61)/sqrt((0.61*(1-0.61))/300] = 1.42 n P(Z < 1.42 ) = 0.9222 [using Excel function NORM.S.DIST(1.42) or Normal table] P-value = 2*P(Z>1.42) = 2*0.078 = 0.156 Decision Rule : Reject H0 if P-value <a. Here a = 0.01 Conclusion: By decision rule, we fail to reject HO

D. Do not reject Ho. There is not sufficient evidence at the a = 0.01 level of significance to conclude that the proportion of ten who are living alone has changed.