Question

A variable of a population has a mean of u = 70 and a standard deviation of a = 7. a. Identify the sampling distribution of the sample mean for samples of size 49. b. In answering part (a), what assumptions did you make about the distribution of the variable? c. Can you answer part (a) if the sample size is 16 instead of 49? Why or why not? a. What is the shape of the sampling distribution? normal a bimodal 0 skewed 0 uniform What is the mean of the sampling distribution? (Simplify your answer.) What is the standard deviation of the sampling distribution? 0:-(Simplify your answer.) b. In answering part (a), what assumptions did you make about the distribution of the variable? O A. It was assumed that the distribution of the variable was unimodal. OB. No assumptions were made because, for a relatively large sample size, the sampling distribution is normal, regardless of the distribution of the variable under consideration. OC. It was assumed that the variable was normally distributed. OD. No assumptions were made because the sampling distribution is normal, regardless of the distribution of the variable under consideration.

Answer 1

Let variable es x. so E(X) = 70 wanaSDOX)=o=7 sample size =49. sampling distribution will be will be normal. per central limit the coram. correct opsion es get bnormats E(x) = and SD (x)=o. then for large samples (230) x = N(M, a 2 (where n is sample size] so E (x) = Mix - 70 SD (T) = 0 1 199 Mix = 70 1