Question

In: Statistics and Probability

A variable of a population has a mean of muμ equals=75 and a standard deviation of...

A variable of a population has a mean of

muμ equals=75

and a standard deviation of

sigmaσ equals=18

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

36

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

36​?

Why or why​ not?

What is the mean of the sampling​ distribution?

Solutions

Expert Solution

Solution :

Given that,

mean = = 75

standard deviation = = 18

n = 36

The sampling distribution of mean and standard deviation is ,

= 75 and

= / n = 18 / 36 = 18 / 6 = 3

n = 25 instead of 36

= 75 and

= / n = 18 / 25 = 18 / 5 = 3.6

If we decrease the sample size the mean of the sampling distribution is the same and standard deviation of the sampling distribution is increases .


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