Question

The grade point averages​ (GPA) for 12 randomly selected college students are shown below. Complete parts​ (a) through​ (c) below. Assume the population is normally distributed. 2.3 3.3 2.7 1.8 0.9 4 2.2 1.4 3.9 0.5 2.3 3.2 (a) Find the sample mean=    (Round to two decimal places as​ needed.) (b) Find sample Standard deviation=   (Round to two decimal places as​ needed.) (C) construct 90% confidence interval=    _ , _   (Round to two decimal places as​ needed.)

Answer 1

Part a

Sample mean = 2.38

Part b

Sample standard deviation = 1.11

Part c

Confidence interval for Population mean is given as below:

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

From given data, we have

Xbar = 2.38

S = 1.11

n = 12

df = n – 1 = 11

Confidence level = 90%

Critical t value = 1.7959

(by using t-table)

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

Confidence interval = 2.38 ± 1.7959*1.11/sqrt(12)

Confidence interval = 2.38 ± 0.5755

Lower limit = 2.38 - 0.5755 = 1.80

Upper limit = 2.38 + 0.5755 = 2.96

Confidence interval = (1.80, 2.96)