Question

the grade point average for 8 randomly selected college students is: 27, 2.9, 3.2, 3.4, 2.9, 4.0, 2.3, 3.5.

a) find the sample mean. (show all work)

b) find the sample standard deviation

c)construct a 95% C.I. for the population mean

Answer 1

Part a

Formula for sample mean is given as below:

Mean = Xbar = ∑X/n

Calculation table is given as below:

No.	X	(X - Xbar)^2
1	2.7	0.17015625
2	2.9	0.04515625
3	3.2	0.00765625
4	3.4	0.08265625
5	2.9	0.04515625
6	4	0.78765625
7	2.3	0.66015625
8	3.5	0.15015625
Total	24.9	1.94875
Mean	3.1125

Sample mean = 24.9/8 = 3.1125

Part b

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

Sample standard deviation = sqrt(1.94875/(8 – 1))

Sample standard deviation = sqrt(1.94875/7)

Sample standard deviation = 0.52762947

Part c

Confidence interval for Population mean

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence level = 95%

n = 8

df = n – 1 = 8 – 1 = 7

Critical t value = 2.3646

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 3.1125 ± 2.3646*0.52762947/sqrt(8)

Confidence interval = 3.1125 ± 2.3646*0.186545188

Confidence interval = 3.1125 ± 0.4411

Lower limit = 3.1125 - 0.4411 = 2.6714

Upper limit = 3.1125 + 0.4411 = 3.5536

Confidence interval = (2.67, 3.55)