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HW ANSWERS p. 479 #31 and p. 499 #2, 3, 11
31) [pic] = 46/220 = 0.2091 p = 30/220 = 0.1364 n = 220
(a) Ho: p = 0.1364
Ha: p > 0.1364
Conditions:
1) SRS assumed representative
2) np & nq > 10 30 & 190 > 10
3) pop > 10n there are more than 2200 people that were in Utah at that time
Conditions met --> Normal model --> 1 prop Z test
Z = [pic] = 3.1434
P(Z > 3.1434) = 8.352 x 10-4
We reject Ho b/c p-value of 8.352 x 10-4 is less than a = 0.05. We have sufficient evidence that the true % of people dying from cancer in Utah in 1955 is greater than 0.1364. Thus, there is evidence that the death rate from cancer among the movie crew is unusually high.
(B) No, this does not prove anything. It just shows us that we have evidence that the movie crew's death rate from cancer was unusually high.
p. 499
2) (a) Ho: p = 0.5 (p = percent of students who prefer metal)
Ha: p > 0.5
one sided
(b) Ho: p = 0.10
Ha: p ≠ 0.10 two sided
(c) Ho: p = 0.22
Ha: p > 0.22 one sided
(d) Ho: p = 0.60
Ha: p > 0.60 one sided
3) Ho: new = old med
Ha: new > old med
p-value of 0.047
There is a 4.7% chance of getting a sample where the new medication is this much better than the traditional, if there really is no difference in the two meds.
11) [pic] = 0.30 n = 1125
(a)
Conditions:
1) SRS stated random
2) np & nq > 10 338 and 787 > 10
3) pop > 10n there are more than 11250 US adults
Conditions met --> Normal model--> 1 prop Z Interval
0.30 + (1.96)[pic] = (0.27365, 0.32723)
We are 95% confident that the true approval rating for George W. Bush's is between 27.365% and 32.723%.
(b) Ho: p = 0.27
Ha: p > 0.27
Since 0.27 is not inside the interval, it is not a plausible value for p. Therefore we reject the Ho (p = 0.27).
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