Question

A variable of a population has a mean of muequals85 and a standard deviation of sigmaequals6. a. Identify the sampling distribution of the sample mean for samples of size 36. 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 25 instead of 36​? Why or why​ not?

A.

. What is the shape of the sampling​ distribution?

Pick one:

uniform

skewed

bimodal

normal

What is the mean of the sampling​ distribution? Fill in answer

What is the standard deviation of the sampling​ distribution? Fill in answer

b. In answering part​ (a), what assumptions did you make about the distribution of the​ variable? Pick one

A. No assumptions were made because the sampling distribution is​ normal, regardless of the distribution of the variable under consideration.

B. It was assumed that the distribution of the variable was unimodal.

C. It was assumed that the variable was normally distributed.

D.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.

c. Can you answer part​ (a) if the sample size is2525 instead of 3636​? Why or why​ not?

Pick one

A.

​Yes, because the sample size must be less than 30 if the distribution of the variable is unknown.

B.

​Yes, because the sample size makes no difference in determining the sampling distribution.

C.

​No, because the sample size needs to be at least 30 if the distribution of the variable is unknown.

D.

​No, because the sample size must be less than 5 if the distribution of the variable is unknown.

Answer 1

What is the shape of the sampling​ distribution?

normal

What is the mean of the sampling​ distribution?

85

What is the standard deviation of the sampling​ distribution?

sigma/sqrt(n) = 6/sqrt(36) = 1

b. In answering part​ (a), what assumptions did you make about the distribution of the​ variable?

D.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.

c. Can you answer part​ (a) if the sample size is2525 instead of 3636​? Why or why​ not?

C.

​No, because the sample size needs to be at least 30 if the distribution of the variable is unknown.