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Stat+20+-+HW10+-+solutions

# Stat+20+-+HW10+-+solutions - 6.102 We expect 50 tests to be...

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Unformatted text preview: 6.102. We expect 50 tests to be statistically signiﬁcant: Each of the 1000 tests has a 5% chance of being signiﬁcant, so the number of signiﬁcant tests has a binomial distribution with n = 1000 and p = 0.05, for which the mean is Hp = 50. 6.112. (a) 1:11 : P(Type 1 error): P(f > 26 when ,u : 25) _ 26—25 _ _ _ P(Z > 501m)_ P(Z :> 0.6) _0.2T43. (b) P('Iype 11 error when tr : 28): P(f 5 26 when p‘. : 28) : P(Z 5 537%) : P(Z < —1.2) : 0.1151. (c) P(Type1[errorwhenp.:30):P(f<26when11:30) _ 26—30 _ _ _ _ 13(2 5 5mm) _ 13(2: .; 2.4) _0.0082. (11) The sample size (n = 900) is so large that the mean will be very close to Normal. 6.114. (a) P(Type I error) : P(X : 0 or X : 1 when the distribution is pro) : 0.2. (b) Pﬂ’ype 11 error) = P(X :-.- 1 when the distribution is p1) = 0.6. 2.20. (:1) df = 19. (b) 2.093 s: t c 2.205. (c) 0.02 s: P 4:: 0.025. (d) t = 2.10 is signiﬁcant at 5% but not at 1%. (c) From software, P i 0.0247. 7 .24. (a) A stemplot (shown) or a histogram shows no outliers and no particular 3 4 skewness. (In fact, for such a small sample, it suggests no striking deviations g 377 flem Normality.) The use of 1 methods seems to be safe. ([1) The mean is 4 1 f i 43.111r mpg, the standard deviation is s i 4.4149 mpg, and the standard 4 23333 error is SIR/E i 0.98'1'2 mpg. For df : 19, the 2.5% critical value is 4 445 r“ i 2.093, so the margin of error is as NE 2 2.0662 mpg. (13) The 95% j: 337 conﬁdence interval is 41.1038 to 45.2362 mpg. 5 D 7.32. (a) & (b) For example, the weight change for Subject 1 is 61.”.Ir — 55.1Ir : 6 kg. The mean change is f : 4.73125 kg and the standard deviation is s i 1.745? kg. ((3) SE— : s/JE i 0.4364 kg; for df : 15,1r“ : 2.131, so the margin of mm for 95% conﬁdence is i0.9300 (software: :l:0.9302). Based on a method that gives correct results 95% of the time, the mean weight change is 3.8012 to 5.6613 kg (software: 3.8010 to 5.6615 kg). (11) f : 10.408115 1b, .9 i 3.8406 1b, and the 95% conﬁdence interval is 8.3626 to 12.4549 lb (software: 8.3622 to 12.4553 lb). (13) H0 is p. = 16 1b. The test statistic is t i —5.823 with (if : 15, which is highly signiﬁcant evidence (P <: 0.0001) against H0 (unless Ha is p. :— 16 lb). (1‘) The data suggest that the excess calories were not converted into weight; the subjects must have used this energy some other way. (See the next exercise for more information.) ...
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