Unit 4 Extra Credit: Problem 5 (1 point) Like the formulas for the hypothesis tests about a single population parameter, the formulas for the hypothesis test about the difference in population means are based off of the sampling distribution for (1 f2). 2 2 _ _ 0' 0' The sampling distribution of (x1 x2) has a mean of #8142) = y] M2 and a standard deviation of 0'61_}2) = 1 + 2 . "1 "2 0' Recall that under the Central Limit Theorem, the distribution of sample means has a mean of [4; = M and a standard deviation of 0'; = T n (a) Suppose the first sample of 100 observations is selected from a population with mean \"1 = 180 and variance of = 1070. Construct an interval extending 2 standard deviations of the mean of the sampling distribution of 351 . 5/413 (b) Suppose the second sample of 100 observations is selected from a population with mean #2 = 180 and variance 0% = 1160. Construct an interval extending 2 standard deviations of the mean of the sampling distribution of E2. $1423 (c) Consider the difference between the two sample means (E1 $2). Compute the mean and the standard deviation of the sampling distribution of (El f2). mean = standard deviation = (d) Based on 100 observations, construct an interval extending 2 standard deviations of the mean of the sampling distribution of (f1 2) S(M1-M2)S