Question

4) Find the degrees of freedom and critical value ?? for the confidence level ? = 0.95 and sample size ? = 21.

5) A random sample of high school boys were asked how many hours per week they play video games. The sample mean of the 32 boys was 12. Researchers believe the population standard deviation is 2.9. What is the 90% confidence interval for the true mean for the hours per week high school boys play video games?

Answer 1

Solution :

4)

Given that,

n = 21

Degrees of freedom = n - 1 = 21 - 1 = 20

c = 0.95

= 1 - c = 1 - 0.95 = 0.05

/ 2 = 0.025

t 0.025, 20 = 2.086

Critical value = 2.086

5)

At 90% confidence level the z is ,

= 1 - 0.9 = 0.10

/ 2 = 0.05

Z/2 = 1.645

E = Z *

= 1.645 * 2.9 / 32

= 0.84

The 90 % CI of mean is

Sample mean +/- 0.84

12 +/- 0.84

(11.16 , 12.84)