Question

a variable of a population has a mean of 79 and a standard deviation of 18.

a. Identify the sampling distribution of the sample mean for samples of size 81.

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 ​81? Why or why​ not?

a. What is the shape of the sampling​ distribution? uniform bimodal skewed normal?

What is the mean of the sampling​ distribution? ​(Simplify your​ answer.)

What is the standard deviation of the sampling​ distribution? ​(Simplify your​ answer.)

b. In answering part​ (a), what assumptions did you make about the distribution of the​ variable? 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 variable was normally distributed. C. 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. D. It was assumed that the distribution of the variable was unimodal.

c. Can you answer part​ (a) if the sample size is 25 instead of 81​? Why or why​ not? A. ​Yes, because the sample size makes no difference in determining the sampling distribution. 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 must be less than 30 if the distribution of the variable is unknown. D. ​No, because the sample size needs to be at least 30 if the distribution of the variable is unknown.

Answer 1

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