For the following situation, find the mean and standard deviation of the population. List all samples (with replacement) of the given size from that population and find the mean of each. Find the mean and standard deviation of the sampling distribution and compare them with the mean and standard deviation of the population.

The scores of three students in a study group on a test are

96,

95,

97.

Use a sample size of 3.

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Part 1

The mean of the population is

enter your response here.

(Round to two decimal places as needed.)

Part 2

The standard deviation of the population is

enter your response here.

(Round to two decimal places as needed.)

Part 3

Identify all samples of size 3 with the correct accompanying means below.

A.

95,95,96

x=95.33

B.

95,96,95

x=95.33

C.

95,97,95

x=95.67

D.

96,95,95

x=95.33

E.

96,96,96

x=96

F.

95,96,97

x=96

G.

95,97,96

x=96

H.

96,97,95

x=96

I.

96,95,96

x=95.67

J.

96,97,96

x=96.33

K.

97,97,95

x=96.33

L.

97,96,96

x=96.33

M.

96,96,97

x=96.33

N.

95,95,95

x=95

O.

97,95,95

x=95.67

P.

97,97,97

x=97

Q.

97,97,96

x=96.67

R.

97,96,95

x=96

S.

96,97,97

x=96.67

T.

97,95,97

x=96.33

U.

97,96,97

x=96.67

V.

95,96,96

x=95.67

W.

96,96,95

x=95.67

X.

96,95,97

x=96

Y.

95,97,97

x=96.33

Z.

95,95,97

x=95.67

[.

97,95,96

x=96

Part 4

The mean of the sampling distribution is

enter your response here.

(Round to two decimal places as needed.)

Part 5

The standard deviation of the sampling distribution is

enter your response here.

(Round to two decimal places as needed.)

Part 6

Choose the correct comparison of the population and sampling distribution below.

A.

The means are not equal and the standard deviation of the sampling distribution is larger.

B.

The means are equal but the standard deviation of the sampling distribution is smaller.

C.

The means and standard deviations are equal.

D.

The means are not equal and the standard deviation of the sampling distribution is smaller.

E.

The means are equal but the standard deviation of the sampling distribution is larger.