Question

Use Table V in Appendix A to determine the t-percentile that is required to construct each of the following two-sided confidence intervals. Round the answers to 3 decimal places.

(a) Confidence level = 95%, degrees of freedom = 19

(b) Confidence level = 95%, degrees of freedom = 30

(c) Confidence level = 99%, degrees of freedom = 17

(d) Confidence level = 99.9%, degrees of freedom = 14

Answer 1

Solution :

Given that,

(a) Confidence level = 95%, degrees of freedom = 19

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,19 = 2.093

(b) Confidence level = 95%, degrees of freedom = 30

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,30 =2.042

(c) Confidence level = 99%, degrees of freedom = 17

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.001 / 2 = 0.005

t _/2,df = t_0.005,17 =2.898

(d) Confidence level = 99.9%, degrees of freedom = 14

At 99.9% confidence level the t is ,

= 1 - 99.9% = 1 - 0.999 = 0.001

/ 2 = 0.001 / 2 = 0.0005

t _/2,df = t_0.0005,14 = 4.140