Question

group and a placebo group. The pution and consume that the population and esh t e me the two Samples are independent com a Computers and be Us 0.05 picancello c ted from Placebo OS

Answer 1

a) Correct answer: Option (A)

b)

Since it is assumed that the population variances are unequal, the t-statistic is computed as follows: t=47-X V Vn 2.37 - 2.65 = -1.458 / 0.842 V 25 T 0.552 35

Answer: t = -1.46

The p-value is p = 0.153

Since p-value > alpha 0.05 so we accept H0

Correct answer: Option (A)

b)

Based on the informationa provided, we assume that the population variances are unequal, so then the number of degrees of freedom is computed as follows: df = (sini+sina) - - 2 = 39.548 The critical value for a = 0.05 and df = 39.548 degrees of freedom is te = t1-a/2.n-1 = 2.022. The corresponding confidence interval is computed as shown below! Since we assume that the population variances are unequal, the standard error is computed as follows: se = V mi ne 0.842 0.552 = 125 + 35 = 0.192 Now, we finally compute the confidence interval: CI = = (X1 - X-te x se, X1 - 2 +te x se) (2.37 -2.65 - 2.022 x 0.192, 2.37 – 2.65 +2.022 x 0.192) = (-0.668, 0.108)

The 95% confidence interval is −0.668 < μ_1​−μ₂​ < 0.108