A variable of a population has a mean of =76 and a standard deviation of =21.

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 thevariable?

c. Can you answer part(a) if the sample size is 16 instead of 49? Why or whynot?

a. What is the shape of the samplingdistribution?

bimodal

uniform

normal

skewed

What is the mean of the samplingdistribution?

x=

nothing

(Simplify youranswer.)

What is the standard deviation of the samplingdistribution?

x=

nothing

(Simplify youranswer.)

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

A.

It was assumed that the variable was normally distributed.

B.

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

C.

No assumptions were madebecause, for a relatively large samplesize, the sampling distribution isnormal, regardless of the distribution of the variable under consideration.

D.

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

c. Can you answer part(a) if the sample size is 16 instead of 49? Why or whynot?

A.

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

B.

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

C.

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

D.

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

Click to select your answer(s).