Question

Find the critical value t_α to be used for a confidence interval for the mean of the population in each of the following situations.

(a) a 95% confidence interval based on n = 12 observations


(b) a 90% confidence interval from an SRS of 22 observations


(c) an 80% confidence interval from a sample of size 40

Answer 1

SOLUTION:

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

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,11 =2.201 ( using student t table)

B.

Degrees of freedom = df = n - 1 =22 - 1 = 21

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,21 = 1.721

C.

Degrees of freedom = df = n - 1 = 40- 1 = 39

At 80% confidence level the t is ,

= 1 - 90% = 1 - 0.80 = 0.2

/ 2 = 0.2 / 2 = 0.1

t /2,df = t0.1,39 = 1.304