Complete parts (a) through (e) for the population data below.

6

6,

7

7,

8

8

a. Find the mean,

mu

, of the variable.

mu

equals

=

nothing

(Type an integer or a decimal.)

b. For each of the possible sample sizes, construct a table with all possible samples and their sample means, and draw a dotplot for the sampling distribution of the sample mean.

Find the sample mean

x overbar

x for each possible sample of size n

equals

=1.

Sample	x overbar x
6 6	nothing
7 7	nothing
8 8	nothing

(Type integers or decimals.)

Draw the dotplot for the sampling distribution of the sample mean for n

equals

=1. Choose the correct plot below.

A.

5

6

7

8

9

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. Three dots are plotted, one each above the horizontal ticks 6, 6.5, and 7.5.

B.

5

6

7

8

9

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. Three dots are plotted, one each above the horizontal ticks 6.5, 7, and 7.5.

C.

5

6

7

8

9

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. Three dots are plotted, one each above the horizontal ticks 6.5, 7.5, and 8.

D.

5

6

7

8

9

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. Three dots are plotted, one each above the horizontal ticks 6, 7, and 8.

Find the sample mean

x overbar

x for each possible sample of size n

equals

=2.

Sample	x overbar x
6 6, 7 7	nothing
6 6, 8 8	nothing
7 7, 8 8	nothing

(Type integers or decimals.)

Draw the dotplot for the sampling distribution of the sample mean for n

equals

=2. Choose the correct plot below.

A.

5

6

7

8

9

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. Three dots are plotted, one each above the horizontal ticks 6.5, 7, and 7.5.

B.

5

6

7

8

9

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. Two dots are plotted, one each above the horizontal ticks 6.5 and 7.5.

C.

5

6

7

8

9

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. Three dots are plotted, one each above the horizontal ticks 6.5, 7.5, and 8.

D.

5

6

7

8

9

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. Three dots are plotted, one each above the horizontal ticks 6, 6.5, and 7.5.

Find the sample mean

x overbar

x for each possible sample of size n

equals

=3.

Sample	x overbar x
6 6, 7 7, 8 8	nothing

(Type an integer or a decimal.)

Draw the dotplot for the sampling distribution of the sample mean for n

equals

=3. Choose the correct plot below.

A.

5

6

7

8

9

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. Three dots are plotted, one each above the horizontal ticks 6.75, 7, and 7.25.

B.

4

5

6

7

8

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 4 to 8 in increments of 1. A dot is plotted above the horizontal tick 6.

C.

6

7

8

9

10

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 6 to 10 in increments of 1. A dot is plotted above the horizontal tick 8.

D.

5

6

7

8

9

x overbar

x

A dotplot has a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. A dot is plotted above the horizontal tick 7.

c. Use the dotplots from part (b) to create one plot with the sampling distributions for each sample size and interpret your results. Choose the correct plot below.

A.

5

6

7

8

9

n equals 3

n=3

n equals 2

n=2

n equals 1

n=1

mu

x overbar

x

Three vertically-stacked boxplots share a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. A vertical dashed line passes through each of the boxplots at horizontal tick 7. The first boxplot labeled "n equals 3" contains one dot at 7. The second boxplot labeled "n equals 2" contains three dots, one each at 6.5, 7, and 7.5. The third boxplot labeled "n equals 1" contains three dots, one each at 6, 7, and 8.

B.

5

6

7

8

9

n equals 3

n=3

n equals 2

n=2

n equals 1

n=1

mu

x overbar

x

Three vertically-stacked boxplots share a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. A vertical dashed line passes through each of the boxplots at horizontal tick 7. The first boxplot labeled "n equals 1" contains three dots, one each at 6, 7, and 8. The second boxplot labeled "n equals 2" contains two dots, one each at 6.5 and 7.5. The third boxplot labeled "n equals 3" contains one dot at 7.

C.

5

6

7

8

9

n equals 3

n=3

n equals 2

n=2

n equals 1

n=1

mu

x overbar

x

Three vertically-stacked boxplots share a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. A vertical dashed line passes through each of the boxplots at horizontal tick 7. The first boxplot labeled "n equals 1" contains three dots, one each at 6, 7, and 8. The second boxplot labeled "n equals 2" contains three dots, one each at 6.5, 7, and 7.5. The third boxplot labeled "n equals 3" contains three dots, one each at 6.75, 7, and 7.25.

D.

5

6

7

8

9

n equals 3

n=3

n equals 2

n=2

n equals 1

n=1

mu

x overbar

x

Three vertically-stacked boxplots share a horizontal x-bar-axis labeled from 5 to 9 in increments of 1. A vertical dashed line passes through each of the boxplots at horizontal tick 7. The first boxplot labeled "n equals 1" contains three dots, one each at 6, 7, and 8. The second boxplot labeled "n equals 2" contains three dots, one each at 6.5, 7, and 7.5. The third boxplot labeled "n equals 3" contains one dot at 7.

Interpret the plot. Choose the correct answer below.

A.

As the sample size increases, the sampling distribution of the sample mean clusters closer to the population mean.

B.

As the sample size decreases, the sampling distribution of the sample mean clusters closer to the population mean.

C.

As the sample size increases, there are more sample means per sample size.

D.

The plot appears random.

d. For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.

n	Probability
1	nothing
2	nothing
3	nothing

(Type integers or simplified fractions.)

e. For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5 or less (in magnitude), that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5.

n	Probability
1	nothing
2	nothing
3	nothing

(Type integers or simplified fractions.)