Question

use StatCrunch for this question)You are studying statistical skills of UAlbany students. You measured statistical IQ in a randomly selected group of 25 UAlbany students. The sample mean statistical IQ in this group is 110 and the sample variance is 144. It is known that the statistical IQ follows a normal distribution.

Construct the 90% two-sided confidence interval for the mean of the statistical IQ

Answer 1

Solution :

Given that,

= 110

s² = 144

s = 12

n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,24 = 1.711

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

= 1.711 * (12 / 25)

= 4.1

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

- E < < + E

110 - 4.1 < < 110 + 4.1

105.9 < < 114.1

(105.9 , 114.1)