A variable of a population has a mean of µ = 75 and a standard deviation of o = 16.a. Identify the sampling distribution of the sample mean for samples of size 64.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 64? Why or why not?a. What is the shape of the sampling distribution?bimodalnormalskeweduniformWhat is the mean of the sampling distribution?= 60 (Simplify your answer.)What is the standard deviation of the sampling distribution?o; = 1.1 (Simplify your answer.) b. In answering part (a), what assumptions did you make about the distribution of the variable?A. It was assumed that the distribution of the variable was unimodal.B. 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. No assumptions were made because the sampling distribution is normal, regardless of the distribution of the variable under consideration.D. It was assumed that the variable was normally distributed.c. Can you answer part (a) if the sample size is 25 instead of 64? Why or why not?O 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 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.

(a) Determine the shape of the sampling distribution. Since, the sample is greater than 30, the sampling distribution of sample mean is approximately normally distributed. Correct option: Option 2 Compute the mean of the sampling distribution. The mean of sampling distribution of the sample mean is obtained below as follows: Thus, the mean of sampling distribution of the sample mean is 64. Compute the standard deviation of the sampling distribution of the sample mean. The Standard deviation of sampling distribution of the sample mean is obtained below as follows: : The Standard deviation of sampling distribution of the sample mean is 2 (b) Determine the assumptions that has made about the distribution of the variable in the part(a). Since, the sampling distribution is approximately normally distributed in spite of the distribution of the variable is unknown no assumptions has been particularly made because of sample size is being large. Correct option: Option B (c ) Determine whether the sample of size 25 can be used instead of 64 in the part(a). It is not possible to consider the sample of size 25 because the sampling distribution cannot be approximately normally distributed since the distribution of the variable is unknown. It is clear that if the sample is relatively large, the sampling distribution is approximately normally distributed in spite of the distribution of the variable. Therefore, the sample of size 25 cannot be used instead of 64 in the part(a). Correct option: Option A

Math

Statistics

A variable of a population has a mean of u = 75 and a standard deviation of o = 16. a. Identify the sampling distribution of the sample mean for samples of size 64. 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 64? Why or why not? a. What is the shape of the sampling distribution? bimodal normal skewed O uniform What is the mean of the sampling distribution? H: = 60 (Simplify your answer.) What is the standard deviation of the sampling distribution? o: = 1.1 (Simplify your answer.)

A variable of a population has a mean of u = 75 and a standard deviation of o = 16. a. Identify the sampling distribution of the sample mean for samples of size 64. 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 64? Why or why not? a. What is the shape of the sampling distribution? bimodal normal skewed O uniform What is the mean of the sampling distribution? H: = 60 (Simplify your answer.) What is the standard deviation of the sampling distribution? o: = 1.1 (Simplify your answer.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

A variable of a population has a mean of µ = 75 and a standard deviation of o = 16.
a. Identify the sampling distribution of the sample mean for samples of size 64.
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 64? Why or why not?
a. What is the shape of the sampling distribution?
bimodal
normal
skewed
uniform
What is the mean of the sampling distribution?
= 60 (Simplify your answer.)
What is the standard deviation of the sampling distribution?
o; = 1.1 (Simplify your answer.)

b. In answering part (a), what assumptions did you make about the distribution of the variable?
A. It was assumed that the distribution of the variable was unimodal.
B. 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. No assumptions were made because the sampling distribution is normal, regardless of the distribution of the variable under consideration.
D. It was assumed that the variable was normally distributed.
c. Can you answer part (a) if the sample size is 25 instead of 64? Why or why not?
O 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 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.

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