In: Statistics and Probability
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 160out 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 1834young 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 | 160 | 813 | 0.19680 |
2000 | 288 | 1834 | 0.15703 |
SE = 0.01580
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 0.05 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 δp 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 H0
fail 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.