Question

QUESTION 25 4 poin Problem 25) For a project that investigates the average weight difference by gender of patients from the Mayo clinic the researcher collected a sample of 64 male patients and another sample of 36 female patients. The researcher then calculated the sample mean of male patients as 160 lbs with a sample standard deviation of 20 lbs, and the sample mean of female patients as 140 lbs with a sample standard deviation of 10 lbs. Test the claim that the average weight of male patients is more than that of female patients. Assume unequal population standard deviation. Given the significance level equals 5. (Question), Step 5: Conclusion: There is enough evidence to conclude that the average weight of male patients is more than that of the female patients at 0.05. True/False True O False

Answer 1

we havre population - II (female) populuhon-T (Male) Sample size, n = 64 Sample mean the = 160 lbs Sample standard Sample size na = 36 Sample mean n = 140 lbs Sample standard deviation B2 = 10 lbs deciation - 20 lbs let (Miro) and (4262) denoter means and standard deciation of male and female population respectively Here we wants to test Roma Mull bypothesis Ho! 4 = 42 ie average weight of male patients and female patients equal Alternative than hippothesis H, 4, > 42 ie average weight of male patients in greater average weight of female pabients. Assumphron (1) since sample size sufficiently large so we can use normal approximation (ii) population variances are unequal (6276)

To test oboue mentioned by botherio, test statistie is given *- , - (41,-) ~1/01) 12 Under Ho (4,5 M2) =) 2= na since 2 and 62 are unknow, replace them with their sample madogues. sit and the Then test statistic under Ho is girien as 7,- ) z = - ~ N(0,1) 2 si B2 + m2 ni let us calulate, z for grien observation 160-140 Z[calculated) 400 64 + 36 6.656

X=0.05 form standard Normal variate table for tabulate value of 2-statistic is z (tabulate) 1•645 z (0.05 ) = 1,645 . 0105 Conclusion 22:1-645 since null z (calculate) > 3 [terbululed) So we refect hypothesis and conclude that, there is enough evidence to conclude that the are average weight of male patients is more than that of the the female patient at x=0.05 Statement is Ture