Question

The following sample was obtained from a population

with unknown parameters.

Scores : 6, 12, 0, 13, 4, 7

a. Compute the sample mean and standard deviation.

(Note that these are descriptive values that summarize the sample data.)

b. Compute the estimated standard error for M.

(Note that this is an inferential value that describes how

accurately the sample mean represents the unknown

population mean.)

Answer 1

a. Compute the sample mean and standard deviation.

Sample mean = Xbar = ∑X/n

Sample variance = ∑(X - mean)^2/(n – 1)

Sample standard deviation = sqrt[∑(X - mean)^2/(n – 1)]

The calculation table is given as below:

No.	X	(X - mean)^2
1	6	1
2	12	25
3	0	49
4	13	36
5	4	9
6	7	0
Total	42	120

Sample mean = 42/6 = 7

Sample mean = 7

Sample variance = 120/(6 – 1) = 24

Sample variance = 24

Sample standard deviation = sqrt(24) = 4.898979486

Sample standard deviation =4.8990

b. Compute the estimated standard error for M.

Standard error = Standard deviation / sqrt(n)

Standard deviation = 4.898979486

n = 6

Standard error = 4.898979486/sqrt(6) = 2

Standard error = 2.00