Question

The grade point averages​ (GPA) for 12 randomly selected college students are shown on the right. Complete parts​ (a) through​ (c) below. Assume the population is normally distributed. 2.2 3.2 2.5 1.6 0.6 4.0 2.3 1.3 3.6 0.3 2.3 3.4

a) Find the sample mean.

x overbar x equals=

​(Round to two decimal places as​ needed.)

​(b) Find the sample standard deviation.

s equals=

​(Round to two decimal places as​ needed.)

​(c) Construct a

95​%

confidence interval for the population mean

muμ.

A

95​%

confidence interval for the population mean is left parenthesis nothing comma nothing right parenthesis .,.

​(Round to two decimal places as​ needed.)

Answer 1

Solution :

Using calculator,

(a)

= 27.3 / 12 = 2.28

(b)

s = 1.17

(c)

t _/2,df = 2.201

Margin of error = E = t_/2,df * (s /n)

= 2.201 * (1.17 / 12)

Margin of error = E = 0.74

The 95% confidence interval estimate of the population mean is,

- E < < + E

2.28 - 0.74 < < 2.28 + 0.74

1.54 < < 3.02

(1.54 , 3.02)