Question

Boomerang Generation: The Boomerang Generation refers to the recent generation of young adults who have had to move back in with their parents. In a 2012 survey, suppose 155 out of 803 randomly selected young adults (ages 18-34) had to move back in with their parents after living alone. In a similar survey from the year 2000, suppose 288 out of 1824 young adults had to move back in with their parents. The table below summarizes this information. The standard TICE ANOTHER error (SE) is given to save calculation time if you are not using software. Data Summary: number who total number Proportion Year moved back (x) in survey (o) - (x/n) 2012 155 803 0.19303 2000 288 1824 0.15789 SE = 0.01586 The Test: Test the claim that a greater proportion of all young adults moved back in with their parents in 2012 than in 2000. Use a 0.01 significance level. (a) Letting B, be the proportion of young adults that had to move back in with their parents in 2012 and P2 be the proportion from 2000, calculate the test statistic using software or the formula (P1-P2) - 8 SE where 8p is the hypothesized difference in proportions from the null hypothesis and the standard error (SE) given with the data. Round your answer to 2 decimal places. To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.

Answer 1

Hypothesis:

$\small \\ H_0: P_1 \leq P_2 \\ H_a: P_1 > P_2$

a.

Test statistic,

(R - P2) - (P1-P2) = VP(1 – Þ) (+ + +) 22 = (0.19303 - 0.15789) - 0 0.01586 = 2.22

b.

p-value = P(z > 2.22) = 1- P(z < 2.22) = 0.0132

c.

Since p-value is greater than 0.01, we fail to reject H₀.

d.

There is not enough evidence to support the claim that a greater proportion of all young adults moved back in with their parents.