Inference for 2 proportions Note: P1 = x1/ni and P2 T2/n2; sometimes the problem
ID: 3310206 • Letter: I
Question
Inference for 2 proportions Note: P1 = x1/ni and P2 T2/n2; sometimes the problem will give you P1 and p2 other times you'll get the counts and r2 in which case use these to get the sample proportions pi and p2. Confidence interval for (p P2) Get z from bottom row of table D (this table is set up for CIs). p-value for Ho: (P1 P2) 0 where p (2)/(ni +n2) if given the counts i and r2 and if sample proportions are given use p-(mpl + n2P2)/(n-+ n2). Take zatat to table A to get the tail area and then the p-value. 8.52 A university financial aid office polled an SRS of undergraduate students to study their summer employment. Not all students were employed the previous summer. Here are the results for men and women: 728 Not employed 89 817 Men Women 603 149 752 ot We are going to find the 99% CI for (p1-p2) where pl (p2) is the population proportion of employed men (women). Note p1 and p2 are defined differently from the previous questions 1, Find (phat1 phat2), Round to 4 digits (eg 0.1234) 2. Find the estimated standard error sehat for the confidence interval. Round to 4 digits (eg 0.1234) 3. Report z* for the 99% CI from Table D. Enter to the accuracy given in the table 4 Find the lower endpoint of the 99% Cl. Round to 3 digits (eg 0.123) 5 Find the upper endpoint of the 99% CI Round to 3 digits (eg 0123) 6. To use the normal approximation to the binomial we have the rule of thumb that np and n(1-p) should both be larger than 10. Check that this is the case by reporting the smaller of these for population 1. This must be an integer 7. Repeat 6 for population 2. Again, this must be an integer. 8. Are n1 and n2 large enough to use the normal approximation. Enter y or n. 9. Using the 99% Cl for p1 p2 do the data reject the claim that the difference in summer employment is 596 at the alpha-0.01 level against a 2-sided alternative. Enter y or nExplanation / Answer
here
1:
p1hat is 728/817
p2hat is 603/752
p1hat -p2hat is 0.08920317
2:
sehat is root( p1*(1-p1)/n1 + p2*(1-p2)/n2 ) is 0.01816828
3:
z* is 2.57897
4:
lower point of the 99% CI is (p1hat -p2hat)-z1*(sehat) is 0.0425238