Question

(1 point) The term Boomerang Generation' refers to the recent generation of young adults who have had to move back in with their parents. In a 2012 survey, 193 out of 801 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, 294 out of 1803 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. total # who moved back (2) z/n year 2012 2000 total # in survey (n) 801 proportion p 0.240948813982522 294 1803 0.1630615640599 Standard Error: SE 0.016557329755233 Test the claim that a greater proportion of all young adults moved back in with their parents in 2012 than in 2000 Test this claim at the 0.05 significance level. (a) Find the test statistic (b) Find the critical value. (c) Find the p-value OYes O No Can you support the claim at the 0.01 significance lever?

Answer 1

Solution: The problem is to test the claim that a greater proportion of all young adults moved back in their parents in 2012 than in 2000. Test this claim at the 0.05 singnificance level.

It is a comparing two proportion kind of probelem.

$p_1$ =Proportion of young adult moved back in their parents in 2012.

$\hat{p_1}=0.240948813982522=0.24(rounded \,\,to \,\,two\,decimal\,places)$

$p_2$ =Proportion of young adult moved back in their parents in 2000.

$\hat{p_2}=0.1630615640599$

Hypothesis to test

$H_0: p_1\leqslant p_2 \,\,\,\, Vs\,\,\,\,\,H_A:p_1> p_2$

Test Statistic :

$Z=\frac{(\hat{p_1}-\hat{p_2})-0}{SE}$

SE=Standard Error =0.016557329755233

$\Rightarrow Z=\frac{(0.240948813982522-0.1630615640599)-0}{0.016557329755233}$

$\Rightarrow Z=4.70409486759213$ =4.7041(rounded to three decimal places )

a) Test Statistic is 4.70409486759213

b) The critical value of upper tailed Z test for $\alpha=0.05$ is given by

0.5-0.05=0.45 and from Z table it is 1.645

c) The P-Value fof test statistic is < 0.00001. It is significant

d) Yes , there are sufficient data to support the claim

e) P-value for significance level 0.01 is  < 0.00001.

Critical value at 0.01 singnificance is given by

0.5-0.01=0.49

from Z table the critical value is 2.326

4.0741 > 2.326

so the test reject the null hypothesis

Yes, i support the claim at 0,01 level of significance

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