A variable of a population has a mean of =73 and a standard deviation of =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 9 instead of 49?

Why or why not?

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Part 1

a. What is the shape of the sampling distribution?

skewed

bimodal

normal

uniform

Part 2

What is the mean of the sampling distribution?

x=________

(Simplify your answer.)

Part 3

What is the standard deviation of the sampling distribution?

x=_____

(Simplify your answer.)

Part 4

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

A.

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.

B.

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

C.

It was assumed that the variable was normally distributed.

D.

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

Part 5

c. Can you answer part (a) if the sample size is 9 instead of 49?

Why or why not?

A.

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

B.

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

C.

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

D.

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