In a previous year, 54% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different tod
ay by conducting a random sample of 700 females aged 15 and older and finds that 369369 are living alone. Is there sufficient evidence at the alphaαequals=0.10.1 level of significance to conclude the proportion has changed? Because np 0 left parenthesis 1-p 0 right parenthesis np01−p0 equals= nothing not equals≠ less than< greater than> equals= 10, the sample size is less than greater than 5% of the population size, and the sample cannot be reasonably assumed to be random, is given to be random, can be reasonably assumed to be random, is given to not be random, the requirements for testing the hypothesis are not satisfied. (Round to one decimal place as needed.) 1. Identify the null and alternative hypotheses for this test. Upper H 0: alpha α p μ greater than> not equals≠ equals= less than< nothing versus Upper H 1: α μ p equals= not equals≠ less than< greater than> nothing (Type integers or decimals. Do not round.) 2. Find the test statistic for this hypothesis test. z 0 equals= nothing (Round to two decimal places as needed.) 3. Determine the P-value for this hypothesis test. P-value equals= nothing (Round to three decimal places as needed.) 4. State the conclusion for this hypothesis test. A. Do not reject Upper H0. There is not sufficient evidence at the alpha α equals=0.10.1 level of significance to conclude that the proportion of females who are living alone has changed. B. Reject Upper H 0. There is sufficient evidence at the alpha equals=0.10.1 level of significance to conclude that the proportion of females who are living alone has changed. C. Reject Upper H 0. There is not sufficient evidence at the alpha α equals=0.10.1 level of significance to conclude that the proportion of females who are living alone has changed. D. Do not reject Upper H0. There is sufficient evidence at the alpha α equals=0.10.1 level of significance to conclude that the proportion of females who are living alone has changed.
