Question

Suppose that a lecturer gives a 10-point quiz to a class of five students. The results of the quiz are 3, 1, 5, 9, and 7. For simplicity, assume that the five students are the population. Assume that all samples of size 2 are taken with replacement and the mean of each sample is found.

Questions:

1. Calculate the population mean and standard deviation
2. Suppose that you obtain at least 20 random samples of size 2. From data obtained by you, find a frequency distribution of sample means and draw a graph (namely, histogram) of the sample means.
3. Confirm whether your histogram appears to be approximately normal.
4. Calculate the mean of sample means and standard deviation of sample means.

Answer 1

Suppose that a lecturer gives a 10-point quiz to a class of five students. The results of the quiz are 3, 1, 5, 9, and 7. For simplicity, assume that the five students are the population. Assume that all samples of size 2 are taken with replacement and the mean of each sample is found.

Questions:

1. Calculate the population mean and standard deviation

Descriptive statistics
n	5
mean	5.0000
population standard deviation	2.8284

2. Suppose that you obtain at least 20 random samples of size 2. From data obtained by you, find a frequency distribution of sample means and draw a graph (namely, histogram) of the sample means.

Data:

sample 1	sample 2	sample mean
3	3	3
3	1	2
3	5	4
3	9	6
3	7	5
1	3	2
1	1	1
1	5	3
1	9	5
1	7	4
5	3	4
5	1	3
5	5	5
5	9	7
5	7	6
9	3	6
9	1	5
9	5	7
9	9	9
9	7	8
7	3	5
7	1	4
7	5	6
7	9	8
7	7	7

sample Mean x	Frequency
1	1
2	2
3	3
4	4
5	5
6	4
7	3
8	2
9	1
Total	25

3. Confirm whether your histogram appears to be approximately normal.

Yes, histogram appears to be approximately normal.

4. Calculate the mean of sample means and standard deviation of sample means.

Descriptive statistics
	mean
mean	5.0000
sample standard deviation	2.0412
sample variance	4.1667