Answers to the Additional Review questions from the text

Review Exercise Answers (Chapter 10)

2.(a) 112. 115 is 1 SD above average at age 18, so the estimate at age 35 is above average by r SDs. This is 0.8 x 15 = 12.

(b) 112.

3. (a) 64 inches
(b) 62 inches
(c) 63 inches
(d) 63 inches

The husband is 4 inches or 4/2.7 or 1.5 SDs above average in height. The wife is predicted to be above average in height by r x 1.5 = 0.25 x 1.5 = 0.4SDs. This is 0.4 x 2.5 or 1 inch.

5. (a) false, (b) false, r measures association, not causation (c) true, (d) true, the correlation of x and y is the same as the correlation of y and x (e) false like (c).

Review Exercise Answers (Chapter 12)

1. In a run of 1 SD, the regression line will rise by r x SD. The slope is .60 x 20/10 = 1.2 final points per midterm point. The intercept is 55 - 1.2x70 = -29. So the equation is

predicted final score = 1.2 x midterm score - 29

2. Predicted income is (960 per inch) x height - $37,400. Taller people make more money on average. Probably, this reflects other variables in family background; although looking every inch the executive may not hurt. FYI, Bill Gates CEO of Microsoft is 5'6".

Review Exercise Answers (Chapter 26)

1. (a) This is true, please read over p. 481
(b) False. The null says differences are due to chance, the alternative says the differences are real/meaningful (review pages 478-479).

3. Null: the data are like 200 draws from a box with 3 1's and a 0. Where 1= blue and 0 = white. The expected number of blues is 150 and the SE is about 6. The z you get is about -1.3 and the p value is 10%. This is marginal (not 5% or less) and could be due to chance.

4. The TA's null: the scores in his section are like 30 draws at random from a box containing all 900 scores. THere is little difference in drawing with or without replacement because the box is big. The null hypothesis specifies the parameters of the population so 63 (average) and 20 (SD). The expected value is 63 and the SE for 30 draws is 3.65. So z is about -2.2 and the p-value is 1%. The TA's defense is not good...

Review Exercise Answers (Chapter 23, p. 428)

1. No, teachers might have been tempted to put poorer children into the treatment group (in fact, this is what happened; children in the treatment group were significantly smaller in physical size than the controls, which probably biased the study against the treatment).

5. Choose (iii), the salary data has a long, right hand tail, the average is bigger than the median. The total of a list is
number of entries x the average.
The total cannot be computed from a median.

9. Guess 520, using the regression method. YOu have a 68% chance to be right within + or - 86 points.

20. (a) the normal approximation will be too low because the curve is lower than the normal probability histogram at 90.

(b) The approximation will be about right.

22. (a) The observed value is 218/500 or 43.6%; the chance error is 3.6%.

(b) The observed value is 191/500 or 38.2% the chance error is -1.8%

The expected value is 40% and the SE is 2.2% for both a and b.

27. (a) 10.8% (b) 1.4% (c) 8.0% to 13.6% is a 95% confidence interval for the percentage of independents among all registered voters in Hayward.

Review Exercise Answers (Chapter 29, p. 568)

2. The explanation isn't good. The comparison is between baseball players and not about left handers in general. A confounder here needs to be associated with left handnesses among baseball players (since this is where the difference in the study is found) and that it causes higher mortality.

5. False, the data are "cross-sectional" (like a snapshot at one point in time) and not "longitudinal" (when a person is followed over a long period of time). So just because 65 year olds appear to be healthier, doesn't mean the trend will continue when the people 18-64 get to 65. It is also the case that people who drink, smoke and skip breakfast also tend not to make it to 65 so they would never get interviewed.

18. Using a telephone survey tends to exclude the homeless, or the recently homeless and the very poor. On the basis of this, the 3% is probably too low. Also, people may not want to admit they've been homeless in the past.

22. The chance is about 4%. It's like abox with 20 tickets with a 1 and 80 with a 0. THe SE is about 8.94.

26. (a) True (b) True (c) False. THe SD is a large fraction of the average, if the data followed a normal curve there would be some negative distances travelled (d) True (e) False. The population average doesn't have a probability histogram. (f) If you doubled the sample size, the SE would be cut by the square root of 2 or 1.4 THe confidence interval would be about .7 as wide.

38. The quote is misleading. The test tells you the chance of seeing a big difference given the null hypothesis. It doesn't tell you the chance that the null is right given a big difference.