Question

5. A company wanted to show, that their vitamin supplement decreases the recovery time from a common cold. They selected randomly 70 adults with a cold. 35 of those were randomly selected to receive the vitamin supplement. The other group received a placebo. The data on the recovery time for both samples is shown below. Drug Sample size Sample mean Sample standard deviation Placebo 35 6.9 2.9 vitamin 35 5.8 1.2 Table 3 Answer the questions below: (a) Assume the samples come from normal distributions with equal variances. Test the claim of the company using a test statistic approach. (b) Assume the samples come from normal distributions with different variances. Test the claim of the company using a test statistic approach. (c) Using s}/s, which of the two tests above should you use to conclude the test hypothesis? (d) Referring to your test statistics from part (a) and (b), what conjecture do you believe you can make?

Answer 1

Solution :- that there 13 a in in the present question, we arould like to check significant diffeence having vitamin tablets Over placebo situratins. in a two different clearly, we have n = 35 X = 6.9 some pele S, - 2.9 S2 = 1.2 12 35 X = 5.8 Normal Assurning that the sample came poples. with aquel raciance from Then the test statistic is, t = x - 52 S.e. (ñ, _ña) ot. n. 92-2 where S.e. (n. 22) - (0 - 1) 8,2 + (2-1)822 n, t02-2

Sub the values , we have, t = 6.9 5.8 34 x Q-9)2+34(1.a) 68 2.074 Now, we calculate the p-value for the obtained and Corresponding t-Statistic . 0.0419 0.05 we see Since the p-value is less than there is a that there is significant placebo. difference between vitamin and (b Assuming that the equal that the popin variance all not , we have the test statistic, F = 3,2 32 Fanna-2

The Values the corresponding substituted, of and we obraun F = (2.92 (1.22 = 5.84 less than 0.05, The p-value is obtained to be We syect the nell hypothesis and we significant difference bow. hence See a that there nitamin. placebo and the f- test for For 82/2, we use use the 2nd test. coe the analysis. Hence See that there is btoo. In both the test, we significant difference is satisfied ploubo and blamin Hence the claim