a The sampling distribution of the sample mean for samples o

a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean  and standard deviation .

b. For part (a) to be true, what assumption did you make about the distribution of the variable under consideration?

A. Uniform distribution.
B. Normal distribution.
C. No assumption was made.

c. Is the statement in part (a) still true if the sample size is 16 instead of 49? Why or why not?

A. Yes, the sampling distribution of the sample mean is always normal.
B. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.
C. No, the sampling distribution of the sample mean is never normal for sample size less than 30

A variable of a population has a mean of Sigma = 21 . a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean and standard deviation . b. For part (a) to be true, what assumption did you make about the distribution of the variable under consideration? A. Uniform distribution. B. Normal distribution. C. No assumption was made. c. Is the statement in part (a) still true if the sample size is 16 instead of 49? Why or why not? A. Yes, the sampling distribution of the sample mean is always normal. B. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true. C. No, the sampling distribution of the sample mean is never normal for sample size less than 30 Mu = 150 and a standard deviation of

Solution

Given that mu = 150, sigma = 21

For answering this question we recollect the central limit theorem for distributions.

As sample size becomes large due to law of large numbers, the sample mean approximates to normal distribution irrespective of the underlying distribution originally.

Hence no assumption was made.

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C. No, the sampling distribution of the sample mean is never normal for sample size less than 30.

Central limit theorem applies only to large numbers and n should be atleast 30. If less than 30, better use t test.

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