Chapter 11 Solutions

Problem 3.

The proportion of surgical operations requiring an overnight stay is 0.40; the risk is the same; The odds of having to stay at the hospital overnight versus getting to go home on the same day are 2 to 3.

Problem 5.

(a) Relative risk = 1.25

(b) The baseline risk is missing.

Problem 6.

(a) observational study

(b) Reasons 3,4, and 5 are all possibilities.

(c) A person who has to fire someone or is subjected to a high-stakes deadline has double the odds of having a heart attack in the following week compared to someone whos has not had to do these things. Although someone who has to fire someone or who has h high stakes deadline has twice the risk of having a heart attack during the next week as someone who has not done those things, the increased risk is quite small. A person who has to fire someone or is subjected to a high-stakes deadline has twice the risk of having a heart attack in the following week compared to someone whos has not had to do these things.

Problem 14.

(a) For the combined table 45% of men were admitted, while 35% of women were admitted, so it appears that women were discriminated against.

(b) Program A admitted 61.5% of the men and 67% of the women. Program B admitted 14.3% of the men and 29.4% of the women. Therefore it appears that men were discriminated against.

Simpson's Paradox occurs when combining groups reverses (or changes substantially) the direction of the relationship from what it was when the groups were separate. In this case, both programs admitted a higher proportion of women than men, yet overall a lower proportion of women admitted. What happened was that program B was harder to get into, and was the one for which a majority of women applied. Of Program A, which was easier to get into, only 10% were women.

Problem 15

(b) for bird owners the risk is .4925. For nonbird owners the risk is 0.301.

(c) No this was a case contro study, not based on a random sample from the population. Clearly, we would not find the risk of lung cancer among bird owners in the general population to be 0.49.

Problem 16

The chi-squared statistic is 22.37 which is much larger than 3.84. Therefore the relationship is statistically significant. There is indeed a relationship between bird ownership and lung cancer that is not likely to be due to chance.

Problem 17

(a) 0.28 for males, 0.23 for females, so the propotion of males that helped is higher.

(b) The chi-squared statistic is 8.64 si the relationship is statistically significant. Researchers have found that males are more likely than females to help someone who has dropped a handful of pencils on the elevator, and that the results in the study arestrong enough to generalize them to the population.

(c) No, the results would have not been statistically significant, becasue the chi-squared statistic would have been 0.86. When conducting research to determine the existence of a weak relationship it is important to take a large enough sample.

Problem 18

(a) The odds are 10.6 to 1 for African-Americans and 32.3 to 1 for Caucasians

(b) Odds ratio = 3.04

(c) The data provide overwhelming eidence that there is a relationship between ethnic group and whether or not someone is laid of.

Problem 19

(b) 76.1% of blacks were approved while 84.7% of whites were approved.

(d) Yes, it would pass because it is over 80% or 4/5.

Problem 20

(b) Chi-squared statistic is 2.715

(c) We would now conclude that there is not a statistically significant relationship between ethniity and mortgage approval. Yet the relationship for the full sample was very strong. This example demonstrates the problem with trying to demonstrate a relationship based on a small sample.