3. (a) There should be 50,000 tickets in the box-the box is the population (all 50,000

forms).

(b) Each ticket shows a 0 (gross income under $50,000) or a 1 (gross income over

$50,000).

(c) False: the SD of the box is = 0.4.

(d) True. The draws are the sample.

(e) The number of sample forms with gross incomes over $50,000 is like the sum of 900 draws from the box. The expected value for the sum is 180. The SE for the sum is x 0.4 = 12. The number of sample forms with gross incomes over $50,000 will be around 180, give or take 12 or so. Now 12 out of 900 is about 1.33%. The percentage of forms in the sample with gross incomes over $50,000 will be 20.00%, give or take 1.33% or so. The chance is about 55%.

  (f) Can't be done with the information given. You need to know the percentage of

forms with gross incomes over $75,000. And you can't use the normal curve, because these data are far from normal.

 11. (a) 357, 340.

(b) 71.4%, 68%.

 Comment. The expected value is computed from the box; the observed value, from the sample.

 The total number of interviews is like the sum of 400 draws from a box. The average of the box is 2.38, and the SD is 1.87. The total number of interviews will be around 400 x 2.38 = 952, give or take

 Chapter 21

 2. (a) 99.6%, 0.3 of 1%.

(b) Can't be done: the box is so lopsided that the normal approximation won't

work. (See exercises 5-6 on p.324; exercises 3-4 on p.383.)

 7. Yes. This is like example 1 on p.378: the estimate is based on a simple random

sample.

11. Option (ii) is it. For example, about 95% of the estimates will be right to within 2

SEs, about 99.7% of them will be right to within 3 SEs, and so forth.

 Chapter 23

 4. Can't be done with the information given. This is a simple random sample of households, but a cluster sample of people. The cluster is the household, and people in a household are likely to be similar with respect to commuting. For example, if a household is far from the center of town, all the occupants are likely to have a long commute. The SE is going to be bigger than the SE for a simple random sample of 2500 persons: section 22.5.

(b) True: section 21.3.

(c) The data don't follow the normal curve, but the 68% might be right; you need

the data to tell. (To see that the data don't follow the curve: enrollments can't be negative, but the SD was a lot bigger than the average, so there must have been a long right hand tail.)

(d) False: 325 is not the SD. (The data aren't normal, which is another problem.)

(e) False. The normal curve is being used on the probability histogram for the

sample average, not the data (pp.411 and 418-19).

 Chapter 23 Special Review Exercises

 25. How did they pick the 5 employees? Quite a lot of bias could come in at this stage.

 28. This is a cluster sample, so you can't compute the SE from the information given

(section 22.5).