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.

2.1, 3.1, 2.6, 1.5, 0.6, 4.0, 2.1, 1.1, 3.6, 0.5, 2.1, 3.4

The grade point averages (GPA) for 12 randomly selected college students are shown on the right. Complete parts (a) through (

construct a 90% confidence interval for the population mean

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Answer #1

Given that,

\bar x = 2.23

s =1.16

n = 12

Degrees of freedom = df = n - 1 = 12- 1 = 11

At 90% confidence level the t is ,

\alpha = 1 - 90% = 1 - 0.90 = 0.1

\alpha / 2 = 0.1 / 2 = 0.05

t\alpha /2,df = t0.05,11 = 1.796 ( using student t table)

Margin of error = E = t\alpha/2,df * (s /\sqrtn)

= 1.796* ( 1.16/ \sqrt 12) = 0.60

The 90% confidence interval estimate of the population mean is,

\bar x - E < \mu < \bar x + E

2.23 - 0.60< \mu <2.23 + 0.60

1.63 < \mu < 2.83

( 1.63 , 2.83)

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