Question

In a previous year, 59 % of females aged 15 and older lived alone. A sociologist tests whether this percentage is diferent today by conducting a random sample of 450 females aged 15 and older and finds that 255 are living alone. Is there suficient evidence at the a 0.05 level of significance to conclude the proportion has changed? 5 % of the population size, and the sample 10, the sample size is satisfied. Because npo (1-Po) the requirements for testing the hypothesis (Round to one decimal place as needed.) Enter your answer in the answer box and then click Check Answer 4 Darts remaining Check Anwe Clear All

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Answer 1

Given, x=255 n= 450 Sample proportion, P = ± 2 = 255 = 0.5666. 7 0.5667 450 Porn 0.59 - Po = 1-0.59=0.4) Since npo, a Co-po) is 210, The sample size is greater than 5% of the population and The sample is given to the rondom, The requirements for testing the hypothesis are satisfied. The following null and alternative hypothesis need to be tested Ho po = 0.59 Hai Po 0.59 The test statisti (Noll hypothesis) Calternative hypothesis) Z= þ- po 0.5667 - 0-59 = 1.005 boll-bo) 10.59) (0.41) V 450 n The p-value (2 Tailed) at z=-1.005 is 0.314897 Since p= 0.31489770.05 Do not reject Ho. So, there in not enough evidence to claim that the population proportion of females who are living alone has changed