Review problems

Answers

Ch. 23
3.a)8.7, 0.3
b) 8.7 ± 0.6 miles
4) Can't be done with information given. (SRS of households but cluster sample of people.)
5) 72.1 ± 2.8%
7)(iii), convenience sample
8a) True
b) True
c) Might be true, need data to decide, since the data don't follow the normal curve. (SD is lot bigger than average, indicating long right hand tail)
d) False
e) False
9) 1.7 ± 0.1
10)a) True
b)False
c)True
d)False
e)False
f)True

Special Review exercises, page 428
3a)Yes. Other things being equal, drinkers will have a higher rate of oral cancer than non-drinkers.
b)(ii)
5)(iii) long right tail, average > median.
9)570,68% (using regression method)
10)21%
13)58%
15)For all, about 3%
26)Chance of getting 8 or fewer is almost 0. These jurors were not chosen at random. The number of blacks in the sample should be around 26, give or take 4.4 or so.
27a)10.8%
b)1.4%
c)8.0%,13.6%,among all registered voters in Hayward.

Ch. 26
2a)The data are like 3800 draws made at random with replacement from a 0-1 box of unknown proportions, with 1 = red.
b)47.4%, fraction is more than 47.4%
c)z is about 2.9, P is about 2/1000
d) Yes
3)yes, could be chance
5a)null: average of the box is 7.5 hours, alternative: average is less than 7.5 hours
7)Disagree. Everyone knows that you get therapy on odd days, and so there is temptation to enroll peopl,e on the odd days.
9)Something is wrong. 21.13 is too many SE's away from the EV.
11a)Data like 750 draws form a box that has 0's and 1's which are equally likely to be drawn.
b)z=6/1.83 &asymp 3.3, so P is very small.
c) Median household income went up.

Ch. 27
3a) Two sample z-test, because there are two samples.
b)null: percentage of 1's in the 2005 box= percentage of 1's in the 2000 box, alternative: the percentage of 1's in the 2005 box is smaller than the percentage of 1's in the 2000 box.
c)P is very small, about 0.003, so we reject the null. The test cannot tell us the cause.
4) Need more information to decide.
5) Framing of the question makes a difference. This is like the example in section 4, so you need to do a z-test for the difference. z turns out to be -10.
7)The observed difference is 1.1%, and the SE for the difference is 4.5%, so it could easily be due to chance. Income support does not seem to work.
b) z=-7.5/1.6 &asymp 4.7, so P &asymp 0. Income support apparently makes the prisoners work less.
9)Do a z-test, and the difference is real. Journals prefer positive articles.
10)The test is not legitimate. First-borns and second-borns are dependent.

Ch. 28
2) (ii) : &chi² &asymp 150 on 3 degrees of freedom, so P &asymp 0
6) Probably not. &chi² &asymp 2 on 10 degrees of freedom, so P < 1%.
7) Yes. &chi² &asymp 0.2 on 2 degrees of freedom, so P &asymp 90% (a good fit).

Ch. 29
4) Yes. Refer to section on Data snooping and multiple testing.
5) There is no chance model. Inner planets are not a sample, they are all the inner planets.
9a) The question makes sense, and the difference is an important one.
b)Yes, since we have random samples, but we do not have enough information/knowledge to answer it.
c)Difference is 38%, SE for difference is 2.1%, so z &asymp 18, and P is &symp 0.
11)The question makes sense, but cannot be answered as given, since teh samples are correlated.
12) Seems a bit over the top. Conclusion might be right.

Last modified: Wed Aug 11 11:03:49 PDT 2010