Refer to the figure at the right. At ?-005, can you support the claim that the p
ID: 3054646 • Letter: R
Question
Refer to the figure at the right. At ?-005, can you support the claim that the proportion of women ages 18 to 24 living in parents' homes was greater in 1997 than in 2004? Assume the survey included 12,300 men and 12,000 women in 199 and 13,800 men and 13,700 women in 2004, and assume the samples are random and independent. Percentage of 18-to 24-year olds livi parents homes 1% Ha Pi P Ha P1 SP2 Find the cnitical value The critical value is zo1.65 (Round to two decimal places as needed ) Find the standardized test statistic Z : ? (Round to two decimal places as needed ) Enter your answer in the answer box and then click Check Answer partExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1997< P2004
Alternative hypothesis: P1997 > P2004
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.45464
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.00623
z = (p1 - p2) / SE
z = - 2.41
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is greater than -2.41
Thus, the P-value = 0.992
Interpret results. Since the P-value (0.992) is greater than the significance level (0.05), we cannot reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that the proportion of women ages 18 to 24 living in parents homes was greater in 1997 than in 2004.