(a) The primary difficulty is the lack of a comparison group. Several reasonable explanations can be provided.
(b) explanatory: whether the student had coaching or not;
response: the student's improvement in SAT scores
(c) observational study
(a) explanatory: whether the patient owns a pet or not;
response: whether the patient survives or not
(b) observational study
21-3: Vitamin C and Cold Resistance
(a) explanatory: whether the subject takes vitamin C or not;
response: whether the subject resists a cold or not
(b) controlled experiment
(c) Many reasonable answers are possible.
21-4: Pregnancy, AZT, and HIV ( cont. )
(a) explanatory: whether the mother receives AZT or a placebo (binary);
response: whether the baby is HIV positive or not (binary)
(b) One group of women receives AZT and another group recieves a placebo.
(c) Women should be randomly assigned to one of the two groups.
(d) Women should not know to which group they have been assigned.
(a) One could randomly assign children to become smokers or nonsmokers and observe whether they develop lung cancer.
(b) case-control
(c) cohort
Many reasonable designs are possible.
22-1: Hypothetical Medical Recovery Rates
(a) N: 0.7; O: 0.5
(b) - (h) Answers vary.
(i) Answers vary, but it should not be very unusual to obtain this sample result by random assignment.
(j) Yes, this sample result should be unusual to achieve by random assignment.
22-2: Pregnancy, AZT, HIV ( cont. )
(a) 
: 
= 
; 
: =
(b) 
AZT = .0793; PLAC = .25
(c) c = .1636
(d) z = -4.54
(e) p-value = 0 (virtually)
(f) virtually 0; yes, extremely unlikely to occur by chance alone
(g) The experimental data provide extremely strong evidence that AZT is more effective than the placebo.
22-3: Hypothetical Medical Recovery Rates ( cont. )
(a) sample sizes
(b) - (c) (Asks for prediction)
(d)
|
"Old" treatment sample size |
"New" treatment sample size |
(One-sided) p-value |
Significant at .10? |
Significant at .05? |
Significant at .01? |
|
50 |
50 |
.1473 |
no |
no |
no |
|
100 |
100 |
.0691 |
yes |
no |
no |
|
200 |
200 |
.0180 |
yes |
yes |
no |
|
500 |
500 |
.0005 |
yes |
yes |
yes |
(e) The difference between 60% and 70% is not convincing if very small samples are involved, but it is convincing if large samples are involved.
23-1: Pregnancy, AZT, and HIV ( cont. )
(a) (-.250, -.092)
(b) The proportion of HIV positive babies in the AZT group is less than the proportion of HIV positive babies in the Placebo group by between roughly 9% and 25%.
(c) (-.264, -.077); wider
(d) (.092, .250); this interval is the negative of the interval in (a); the conclusion does not change at all
(a) 1982 = .8233; 1991 = .7884
(b) : 
1982 = 1991; : 1982 1991
(c) z = 4.431; p-value = 0 (virtually)
(d) (.019, 050); no; the interval supports the conclusion that the proportion of drinkers was higher in 1982 than in 1991
(e) observational study
(f) no
23-3: Berkeley Graduate Admissions ( cont. )
(a) : 
= 
:
z = 9.555; p-value = 0 (virtually); yes, the difference is statistically significant
(b) no; this is an observational study in which Simpson's paradox explains the discrepancy: women tended to apply to the tougher programs to get into