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?

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 .

orchestra answered 2 years ago

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