Stat 401: HW 3 answers:
1) Kelley’s rule is based on the standard error of the mean, 1 point each a) 120 (or 121 if you round up). se = 35.45 / sqrt(16) = 8.86, se/3 = 2.95, so report to the one’s digit. b) 120.57. se = 0.984 / sqrt(16) = 0.246. se/3 = 0.082, so report to the one-hundred’ths place.
2) hand calculations, 1 point each a) 9. calculated as 10 – 1 b) 1.61 calculated as variance = s 2 = ((10-1) x 1.53
2 + (5-1) x 1.79
2 ) / (9 + 4) = 33.884 / 13 = 2.606, so s = sqrt(2.606) = 1.61 c) 13. calculated as (10-1) + (5-1) or 15 – 2 d) 0.94, calculated as sqrt(1.53
2 /10 + 1.79
2 / 5) = sqrt(0.8749) = 0.94 e) 0.88, calculated as 1.61*sqrt(1/10 + 1/5) f) 0.77, calculated as (7.513 - 6.832)/0.8818
3) (speed limits and traffic fatalities), 2 points each a) using pooled error variance: T = -3.04, df = 49, p = 0.0038 b) mean difference is an increase of 22.3% in states that increased the speed limit. The se = 7.33
(Note: SAS and R report 1-2, i.e. No – Yes). For this question, reporting -22.3% is also acceptable. c) changing the speed limit increases the fatalities.
Note: the point of this question is most obvious if your answer to b was -22.3%. That is still an increase in fatalities in the states that increased the speed limit. d) the 95% confidence interval for the increase in fatalities if speed limits were increased is (7.6, 37.0)
4) (Grant’s finches), 1 point each a) b) p < 0.001 (Not asked for but T = -4.69, df = 838) c) increase = 0.54, se = 0.11. Note: only positive answer accepted because only that answers the question. That is because the question asked how much did the beak size increase. d) 95% ci = (0.31, 0.76) e) 90% ci = (0.35, 0.73)