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 813 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 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 (n)	p̂ = (x/n)
2012	155	813	0.19065
2000	288	1824	0.15789

SE = 0.01577

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 p̂₁ be the proportion of young adults that had to move back in with their parents in 2012 and p̂₂ be the proportion from 2000, calculate the test statistic using software or the formulaz =

(p̂1 − p̂2) − δp

SE

where δ_p 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.
z =
To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.

(b) Use software or the z-table to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

(c) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀    

(d) Choose the appropriate concluding statement.

The data supports the claim that a greater proportion of all young adults moved back in with their parents in 2012 than in 2000.There is not enough data to support the claim that a greater proportion of all young adults moved back in with their parents in 2012 than in 2000.    We proved that the harder financial times of 2012 caused a greater proportion of young adults to move back in with their parents.We reject the claim that a greater proportion of all young adults moved back in with their parents in 2012 than in 2000.

Answer 1

a)

z = (p1- p2)/SE
= (0.19065 - 0.15789)/0.01577
= 2.08

b)

p value = 0.0189

c)

fail to reject H0

d)

0.There is not enough data to support the claim that a greater proportion of all young adults moved back in with their parents in 2012 than in 2000.