Question

CAPTER 9 PRACTICE 1. The Valley Soft drink Company is experimenting with two different recipes for a new cola. In market tests of both recipes, it was found that 85 of 140 consumers rated the first recipe as good or better, whereas 90 of 155 consumers rated the second recipe as good or better. a) Construct a 95% confidence interval estimate of the difference between the two proportions. b) Use a .05 level of significance to test the claim that the proportions of good or better are the same for both recipes. ( Make sure to state the null and alternative hypothesis and state the conclusion in non-technical tems)

Answer 1

Given - e = 85 ni =140 n2-155 x2 go Pi 85 U ) 0.60714 140 2 - - The 90 155 0.580645 Value of pooled -proportion is- Xit za 85+90 tn. 140+ 155 P = n o o P - 0.5932 Q = 0.40:68 a 2 - 0.05. is given 95 y as . for : CoI P2 is P Pi - Pz- P2-2212 P 9121 nz POLE PA-P2 + Zalz Le. 0.60714 – 0.580645 – 1.96 0.406x0.593/1 [ + 140 * 155 0.6071 -0.5806 +1.96 040C X0.593 140 e -0.08 665 0.13964

required C.I -0.08665 for P.-P2 is f 0.13964) a Te b] To test Ho: The proportions of good or better Same for both recipes j. e P,=P2 Vs H,: The Proportions of good or better not some for both recipes. i.e P, Ž P2 are Test statistics P, - PZ 2 = fpöcht n. 0.60714 - 0.58064 0.5932X0.4068 4 [ 15 Lo ISS Za0.463 decision- since Izl=0.463 < Z412=1.96 accept Ho i.e null bypothesis 50 че conclusion better The proportions of good or Same for both recipes. are