Question

9) The body mass index (BMI) of an individual is a measure used to judge whether an individual is overweight or not. A BMI between 20 and 25 indicates a normal weight. In a survey of 750 men and 750 women, the Gallup organization found that 203 men and 270 women were normal weight. Construct a 90% confidence interval to gauge whether there is a difference in the proportion of men and women who are normal weight.

Answer 1

Sel7 8] We use paired t-test 10 Document Before (x) After (4) d=x-Y for difference of means. Tu s 6 7 8 9 2 o 1503 ooo I 200 . so 3 0 25 0 9 Null Hypothesis does not Ho: spell-checker & reduces spelling error Alternative hypothesis : 1: spell- checker reduces spelling error. Now, n7 a = { = 23 = 2.56 Ed² = 115 n-1 115 - 58.78]] L. - .0275 . Iti= 1 dl = 2.56 2.56 = 2.8972 - 15% 7.0275 7.0275 0.8836 Tabulated too, for (9-1) = 8 df for two-tailed test. is 3.36. Conclusion: Sinde calculated t is less than tubulated t, we may accept the null hypothesis turer's There is no evidence for manufacturer dain.

|DATE: 1 Soing] We use Proportion Jest of significance for Difference of Null Hypothesis : no :P, = P2 = P (say) ic; There is no significant difference in the proportion of men and women who are normal weight Alternative hypothesis: H: P 7 P2 (two-tailed) We are given : n = 750 x = No. of men with normal weight = 203 n2 = 750 x2 = No of women with normal weight = 270 i p= Proportion of men with normal weight - X,/n, = 203/750 = 0.2707 _ b2 = X2/12 = 270/750 : 0.36 Test statistics : 2 = p.-p2 ~ N(0, 1) 1 P = D. p. + D2 P2 = x, +X2 +02 D, +12 473 = 1500 = 1-P = 10.3153 = = 203 + 270 750 +750 0.3153 17- 0.6847 - z = 0.2707 -0.36 70.3153 X 0:68478 ( -0.0893 + 0.0005757 750) = - 3.7208 1750 750

Conclusion: Since 12l = 3.7208 which is greater than Zasto ie; 1.645, it is significant at 10% 1.0.5 Hence no is reputed at 10% level of significance and we conclude than men and women differ significantly as regards to normal weight? 90 % Confidence interval: (p.-p2) I 1.645 S.E of CP, -P2) ..se I 4-22): 2,93 +P Paz +2442 02 0.2707 x 0.7293 + 0.36x0.64 750 7 so 0.1974 t 0.2304 = 0.0239 - Hence, 90% c. I for P, - P₂ are: 10. 2707 -0.36 + 6.1.645x0.0239 -0.0893 € 0.0393 = -0.0499 - 0-12 86 (-0.05 -0.129)