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stats 3022 hw 6 solution

stats 3022 hw 6 solution - 11.19(a The regression equation...

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Unformatted text preview: 11.19. (a) The regression equation is Shae z 3.33 + 0.82 Unfav —i— 0.57 Fav. (1)) Because P < 0.01, we reject H0: 131 3 ﬁg 2 0 in favor of HG: at least one of ,81 and ﬁg 1s nonzero. (c) The estimates of {30, ,61, and 782 are all signiﬁcantly different from 0 (all have P < 0.01). (d) The 1 statistics have df= n — p — 1 x 152 —- 2 — l = 149. 11.26. The three regression equations and associated results are: M Ass’ﬁ'rs = s R2 r P (a) —17.12 + 0.0832 ACCTS 20.19 0.938 10.96 P < 0.0005 (b) —19.90 + 7.680 MSHARE 50.54 0.609 3.53 P = 0.008 (c) w21.45 + 0.0756 ACCTS + 1.158 MSHARE 20.52 0.944 6.44 P < 0.0005 0.86 P m 0.418 12.23. (a) With I = 4 and N m 2290, the degrees of freedom are DFG m I -— l = 3 and DFE = N — I = 2286. (b) MSE = s; 4 4.6656, so F = % = 211% 2 2.5304. (c) The F(3, 1000) entry in Table E gives 0.05 < P < 0.10; software give P & 0.0555. 12.29. (a) Table below (if, s, s; in mg/100 g). (b) To test H0: 721 = 11.3 = M3 = M4 = M5 vs. Ha: not all u,- are equal, we have F = 36774 with df 4 and 5, and P < 0.0005, so we reject the null hypothesis. Minitab output below. (c) Plot below. We conclude that vitamin C content decreases over time. ’6: 50 8 45 Condition n 37 s 5,; 10?, 40 Immediate 2 48.705 1.534 1.085 §35_ One day 2 41.955 2.128 1.505 530 Three days 2 21.795 0.771 0.545 8:3 Five days 2 12.415 1.082 0.765 015 Seven days 2 8.320 0.269 0.190 E10 WW .4? 5 > Immed One Three Five Seven Condition na yels of Variance on VitC Source DF SS HS F p Days 4 2565.72 641.43 367.74 0.000 Error 5 8.72 1.74 Total 9 2574.44 12.56. We have six comparisons to make, and (if = 351, so the Bonferroui critical value with o: : 0.05 is r** z: 2.6533. The pooled standard deviation is 8,, =: VMSE & 1.1958; the differences, standard errors, and t statistics are below. The only nonsigniﬁcant difference is between the two Pyr treatments (meaning the second application of the shampoo is of little beneﬁt). The Keto shampoo mean is the lowest; the placebo mean is by far the highest. 4 ' Dewey; = 0.19102 Dpy1_K = 1.36456 Dpy1_p = —12.0000 SEPy]_py2 = 0.16088 SEpy[_K = 0.16203 SEpy1_P = 0.25265 1‘13“-pr = 1.187 {Pyl—K = 3.421 {Pyl—P = —47.497 DpygiK : 1.17353 Dpy2_P = —12.1910 SEpygiK : 0.16312 \$1352-15 = 0.25334 tpy2_K =: 7.195 Ipy2_p = —-48.121 . D“: = .—13.3646 SEK_p = 0.25407 IK_p = —52.601 12.57. (a) The three contrasts are: W1 = %MPY1+%ILLPY2 + %MK — MP W2 “—'" \$111M + iﬂpyz - MK W3 = MPyi — MPyz (b) The pooled standard deviation is sp their standard errors are in the table. For (2‘1 2 "—12.51 Cg 21.269 (:3 m 0.191 SECl é 0.2355 SE62 +— 0.1413 SEC3 é 0.1609 t1 = —53.17 IQ, = 8.98 13 =1.19 P1 < 0.0005 P2 < 0.0005 P3 i 0.2359 VMSE : 1.1958. The estimated contrasts and example: ' SEC] = SIN/gnu + 5/109 + 33/106 + 1/28 a 0.2355 (c) We test H0: in,- = 0 VS. Ha: Wi 74 0 for each contrast. The r- and P—values are given in the. table. The Placebo mean is signiﬁcantly higher than the average of the other three, while the Keto mean is signiﬁcantly lOWer than the average of the two Pyr means. The difference between the Pyr means is not signiﬁcant (meaning the second application of the shampoo is of little beneﬁt)—this agrees with our conclusion from Exercise 12.56. N 13.7. (a) The plot suggests a possible inter- action because the means are not parallel. (Note that we could have chosen to put dish type on the horizontal axis instead of proximity; either explanatory variable will do.) (b) By subjecting the same in- dividual to all four treatments, rather than four individuals to one treatment each, we reduce the within-groups variability (the residual), which makes it easier to detect between—groups variability (the main effects and interactions). 13.33. (a) Table below, plot on the right. The mean expected price decreases as the number of promotions increases and also as the percent discount increases up to 30%. The expected price is higher for 40% than for 30%. (b) Minitab output on the next page. Both main effects are signiﬁcant, but there was no signiﬁcant interaction. (c) There is strong evidence of a difference in mean expected price based on the number of promotions and the percent 0.5 0 55 consumption —1 Reported minus actual —1.5 Opaque Clear Proximate Less Proximate Proximity One Three Five Seven Number of promotions discount. Speciﬁcally, the two effects noted in (a) are signiﬁcant: More promotions and higher discounts (up to a point) decrease the expected price. There is no evidence of an interaction . Expected price (\$) 40% discount 30% discount 20% discount 10% discount _ Promotions it" s f s f s f s 1 4.423 0.1848 4.225 0.3856 4.689 0.2331 4.920 0.1520 3 4 .284 0.2040 4.097 0 .2346 4.524 0.2707 4.756 0.2429 5 4.058 0.1760 3 .890 0.1629 4.251 0.2648 4.393 0.2685 7 3.780 0.2144 3.760 0.2618 4.094 0.2407 4.269 0.2699 ...
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