Question

ol. Find the critical value a/2 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 98% and sample size 8 Critical value = х Part 2 of 4 (b) For level 99% and sample size 13 Critical value = Part 3 of 4 (c) For level 99.5% and sample size 28 Critical value = Part 4 of 4 (d) For level 95% and sample size 10 Critical value =

Answer 1

Solution :

Given that,

(a)

sample size = n = 8

Degrees of freedom = df = n - 1 = 8 - 1 = 7

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_0.01,7 = 2.998

Critical value = 2.998

(b)

sample size = n = 13

Degrees of freedom = df = n - 1 = 13 - 1 = 12

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_0.005,13 = 3.055

Critical value = 3.055

(c)

sample size = n = 28

Degrees of freedom = df = n - 1 = 28 - 1 = 27

At 99.5% confidence level the t is ,

$\alpha$ = 1 - 99.5% = 1 - 0.995 = 0.005

$\alpha$ / 2 = 0.005 / 2 = 0.0025

t_{$\alpha$ /2,df} = t_0.0025,27 = 3.057

Critical value = 3.057

(d)

sample size = n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

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_0.025,9 = 2.262

Critical value = 2.262