Question

Use Table A.3 to find the critical value 2 t_a/2 needed to construct a confidence interval of the given level with the given sample size:

a. Level 99%, sample size 19

b. Level 90%, sample size 172

Answer 1

Solution :

Given that,

a.

n = 19

df = n - 1 = 19 - 1 = 18

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df = t0.005,18 = 2.878

The critical value t /2 = 2.878

b.

n = 172

df = n - 1 = 172 - 1 = 171

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,171 = 1.654

The critical value t /2 = 1.654