Question

4. A surprising number of young adults (ages 19 to 25) still live in a parent's home. A random sample by the National Institutes of Health included 2253 men and 2629 women in this age group. The survey found that 986 of the men and 923 of the women lived with their parents. Is this good evidence that different proportions of men and women live with their parents? How large is the difference between the proportions of young men and young women who live with their parents? Step 1: State the hypotheses: Define p1, p2, HO and Ha Step 2: Collect the data: Calculate the sample proportions P, and P2 and their difference Step 3: Assess the evidence Use StatCrunch or formulas to find the Z-score and the corresponding P-value Step 4: State a conclusion Use the P-value to make a decision

Answer 1

4. Giveng Menu m, = 2253 and x = 986 12 = 2629 women : and 22 = 923 are men n Step 1: PI and P2 the population proportions and women, respectively. Our thesis is, hypothesis Ho : P = P2 H; ?, # P2 (Two tailed test) Step 2 24 986 : sample propertim, & 0.4376 M 2253 h. 923 0.3511 2629 0.4376 0.3511 0.0865 Test sin tistics o P - P2 POLL I PALE Where, P = 4+22 986 +923 0.3910 ntuz 2253 +2629 = Step 3 Z ə 1-P = 1-0.3910 0.609 0.0865 z = 0.4376 0. 351 0.01400942 0.3910x 0.609 ( 2253 2629 z = 6.174417 6.174 P-value is calculated in R as, 2+ (1- prorm 16.174)) - 0

since, Ho is that Step 4 y >0.05, þ <a rejected Reject Ho. The refore, we conclude evidence enough claun and live parents. to Supp art the there üs that different with their proportion men wowen go (s) n = 1560 and x = 271 Black driver; while driver : 12 10400 and x2 = 598 Step 1 o popn and P2 are the propor ortion for blacke PI and A driver white driver," respectively. Our bypothesi's is Ho: P = P2 Step 2: sample proportion, Vs Hi P = P2 (Two tailed test 27 / 0.1737 24 M 1560 22 598 0.0575 n2 10400 (? - P2) 0.1737 0.1162 0.05 75 = Step 3: Test statistics : Z 8. - where, P=x+22 mtu2 Pal +1 12 0,0727, Q = 1-p-1-0.0727 = 0.9273 (271+598) (1560 + 10400) 16.48322 0, 1737 - 0.0575 0.1162 0.007049592 Z 0.0727 X0.9273 +1 1560 louw zs 16.483

þ value is calculated in R as, 2+CI- puorme (16.483)) Stepy 6 conclusion claus there is evidence since, p < 0.05, Ho is rejected : Reject to Therefore, we conclude that enough to suppist the proportion of black drivers stopped by is statistically significantly significantly different while drivers un calle fornia. that the police than that ag