Question

Using the t tables, software, or a calculator, estimate the values asked for in parts (a) and (b) below. a) Find the critical value of t for a 98% confidence interval with df = 21. t= (Round to two decimal places as needed.) b) Find the critical value of t for a 95% confidence interval with df = 49. t= (Round to two decimal places as needed.)

Answer 1

Solution :

Given that,

a)

df = 21

At 98% confidence level the t is ,

$\alpha$ = 1 - 98% = 1 - 0.98 = 0.02

$\alpha$ / 2 = 0.02 / 2 = 0.01

t_{$\alpha$ /2,df} = t_0.01,21 = 2.52

t = 2.52

b)

df = 49

At 95% confidence level the t is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

t_{$\alpha$ /2,df} = t_0.025,49 = 2.01

t = 2.01