Question

In a previous​ year, 51​% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 550 females aged 15 and older and finds that 287 are living alone. Is there sufficient evidence at the alphaequals0.01 level of significance to conclude the proportion has​ changed? Because np 0 left parenthesis 1 minus p 0 right parenthesisequals nothing ▼ greater than less than not equals equals ​10, the sample size is ▼ less than greater than ​5% of the population​ size, and the sample ▼ is given to be random, cannot be reasonably assumed to be random, is given to not be random, can be reasonably assumed to be random, the requirements for testing the hypothesis ▼ are are not satisfied. ​(Round to one decimal place as​ needed.) Identify the null and alternative hypotheses for this test. Upper H 0​: ▼ mu p alpha ▼ not equals less than equals greater than nothing versus Upper H 1​: ▼ alpha p mu ▼ less than greater than equals not equals nothing ​(Type integers or decimals. Do not​ round.) Find the test statistic for this hypothesis test. z 0equals nothing ​(Round to two decimal places as​ needed.) Determine the​ P-value for this hypothesis test. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) State the conclusion for this hypothesis test. A. Do not reject Upper H 0. There is not sufficient evidence at the alphaequals0.01 level of significance to conclude that the proportion of females who are living alone has changed. B. Do not reject Upper H 0. There is sufficient evidence at the alphaequals0.01 level of significance to conclude that the proportion of females who are living alone has changed. C. Reject Upper H 0. There is sufficient evidence at the alphaequals0.01 level of significance to conclude that the proportion of females who are living alone has changed. D. Reject Upper H 0. There is not sufficient evidence at the alphaequals0.01 level of significance to conclude that the proportion of females who are living alone has changed.

Answer 1