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 99% confidence interval with df = 18. t= (Round to two decimal places as needed.) b) Find the critical value of t for a 98% confidence interval with df = 91. t= (Round to two decimal places as needed.)

Answer 1

Solution :

Given that,

a ) Degrees of freedom = df = 18

At 99% confidence level the t is ,

$\alpha$ = 1 - 99% = 1 - 0.99 = 0.01

$\alpha$ / 2 = 0.01 / 2 = 0.005

t_{$\alpha$ /2,df} = t_0.005,18 = 2.898

The critical value = 2.90

b ) Degrees of freedom = df =91

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_0.01,91 =2.368

The critical value =2.37