A variable of a population has a mean of u= 81 and a standard deviation of o= 32

Question

A variable of a population has a mean of u= 81 and a standard deviation of o= 32.

a. Identify the sampling distribution of the sample mean for samples of size 64.

What is the shape of the sampling distribution? a. skewed b. normal c. bimodal or d.uniform Which one?

What is the mean of the sampling distribution? u-x = ? (Simplify your answer.)

What is the standard deviation of the sampling distribution? o-x= ? (Simplify your answer.)

b. In answering part (a), what assumptions did you make about the distribution of the variable? 1, 2, 3 or 4?

1. 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.

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

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

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

c. Can you answer part (a) if the sample size is 25 instead of 64? Why or why not? Pick from below.

a. Yes, because the sample size must be less than 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. No, because the sample size needs to be at least 30 if the distribution of the variable is unknown.

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

Explanation / Answer

Answer to the question is as follows:

Normal distribution is as follows:

Mean = 81

Stdev = 32

a. n = 64
Shape is sampling distribution is b. normal, as the n>30

Mean of sampling distribution is equal to the mean of population distribution = 81

Standard deviation of the sample is stdev of pop. divided by sqrt(n) = 81/sqrt(64) = 10.125

b. 1 is correct assumption. This only can be assumed when we have large sample size

c. Since n is less than 30 or sample size is less than 30, we can conclude that we can't guess the distribution
if the variable distribution is unknown. If the pop. distribution was given to be normal then we could have made
the assumption that sampling distribution is normal, even under 30 sample size. But here that' not the case/

Option C is correct.

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