Question

Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. n Male BMI Female BMI 1 12 50 50 27.5997 25 6435 8.819325 4.764227 X S a. Test the claim that males and females have the same mean body mass index (BMI). What are the null and alternative hypotheses? O A. HO 11-12 H₂ 4742 OC. Ho H1 H2 H₂ HH2 ов. Но на * HH12 OD. Ho H12 H H1 H2 The test statistic, t, is 1.38 (Round to two decimal places as needed.) The P-value is 17 (Round to three decimal places as needed.) State the conclusion for the test. Then

Answer 1

Data let, ell be the mean body mass index (BMI) of mate female body mass index (BMI) el2 be the mean given that, 5 E 50 12:50 X1 = 27. 5997 7 = 25. 6435 5,= 80819325 S2= 40764227 Assume that population so are equal Cle @ claim i- Test that males and females who megn body mass index (BMI). 6 = 62) have the same The null and a Hernative hypotheses are, Ansi- A Hoi ella e12 vs Hii el, 82 test statistle, tcal (X; X2 ) -(41,-2) N tn tn, -2 under Ho. S + 1 ni where, § = (n-1) s ' + (02-1) 32² ni+n2-2 .: 3² = 49(8.81932732 + 49(40764224)? 50450-2 CS

S = 50.299126 S: 76087960 tal = (27.5997-25.6435)-0 - 7.087960 ㅗ ГО 5o itcal = 1038 The test statistic t is 1.38 p-value = Pl t < -1:38) * P (t7138) PC t > 1,38) + pctyl:38) a ty on paris symmetric = ex pt 1.38 2x 0. 08537 pevalue=00171 Here, given that, significance level 12) o'os (58) P-value XL (1.0.5), i e o.lll 70.05 fail to reject Ho at $ to level of significance ع کیا conclusioni o fail to reject the null hypothesis there is not sufficient evidence to warrant rejection of the claim the claim that men and women have the same mean BRI Ics

The 95%. for fexprele) iş ( 1&1 - 22 ) ; t 212, dat ne-2 XS / 1 + 1 - 2 significance level (2)= 0.05 tala, ni+02-2 toos_, 982 16984467 Required a lif, (( 2765997 - 2566435 2506435 ) 7 1984467 x 7.081960 so 50 (-0.857, 40769) Ans: 1-0.857 (el-112 [4.769 conclusion - Yes, because the confidence interval contains Zero CS sannel with Os me Sanat