Question

Find the critical value

t/α2

needed to construct a confidence interval of the given level with the given sample size. Round the answers to three decimal places.

Part 1 of 4

(a) For level  

95%

and sample size  

7

Criticalvalue=0

Part 2 of 4

(b) For level  

98%

and sample size  

12

Criticalvalue=

Part 3 of 4

(c) For level  

99%

and sample size  

27

Criticalvalue=

Part 4 of 4

(d) For level  

98%

and sample size  

14

Criticalvalue=

Answer 1

Solution :

Given that,

a ) n = 7

Degrees of freedom = df = n - 1 = 7 - 1 = 6

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_0.025,6 = 2.447

The critical value = 2.447

b)n =12

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

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_0.01,11 =2.718

The critical value =2.718

c )n = 27

Degrees of freedom = df = n - 1 = 27 - 1 = 26

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_0.005,26=2.779

The critical value =2.779

d )n = 14

Degrees of freedom = df = n - 1 = 14 - 1 = 13

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_0.01,13 =2.650

The critical value =2.650