Question

3. Conduct a Pearson Chi-Square test to determine if there is any relationship between diet and outcome. 4. Compute a 95% confidence interval on the proportion of people who are healthy on the AHA diet.

Answer 1

Solution to Q3 cue have the following attributes - K=2 lents (12) Type of Diet haning various outcome measures of health and disease haning b = 4 lenets. Denote : th fij with = frequency in (i, j)th cell corresponding popu ulation proportion bij i=1,2,.,k =1,2,.gl ] l fio = [fij, bio izl, ok - 2 2 E bij jal js, foj 11 Žfis , poj= ² pij ej el, el jai i=1 и e ke Z I fij f = 1 =n= sample size. ΣΣΡ; isljal izija To test Hoi Diet and outcome are independent Not against Hii Ho ie, Ho bij Pioko; & (ij) against H,: Not Ho, we perform a Pearson chi-square test of independence test statsth is ginen sy- The appropriate test stats the k T ŹŹ () - foton X X (R-32-4) i=1 j=1 fiofa

Rule: we reject Ho against hi at leul x Tobs L; (kalla) distribution, X x : upper a point of a Turnent where Li(kalla) Calculations fil = 15 , f12=24, fiz =25, fin = 239 fai = 7, f22 14, f23= 8. fan = 273 2 38 , f20² = 302, foz = 2 fio = 303, foi = 22 foz = 33, fou 512 = Tobs = 1.439 + 1.297 +4.344 +1.184 +1.444 +1.301 + 4.358 + 1. 188 - 16:554 Hore & = 0.05 xon 7.814278 (using qchisqe) im R) 0.05; 3 command in Conclusion > Xossip = 7.814278 Since = 16.554 Tobs 0.05;3 neject Ho against hi at aast. lend of significance and conclude on the basis of the ginen data that significant relationship outcome and diet there is among

Solution to an Total sampled individual having AHA diet (n) 303. Frequency of individual waning meaning who are healthy (f) 239 healthy the Let in true proportion of people le who are 'pi AHA diet be A Define Р sample prop ortion =f A 100(1-2) confidence interval for p is ginen by :- ô claê Mala ê (1-ê 1/2 where aa upper a point of No, 1) distribution, Calculations Ginem, f = 239, n-303 A P f 239 303 Here, 0.05 M 20.025 command in R) Thus a 0.05 = 1.959964 (using quorm) 95% ca for p is given by :- (0.7887789 0.045 95927 , = (0.7428196 0.8347381 (0.7428 0.8347) (Ams) (Rounded to 4 decimas 0.7887789 +0.04595927)