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.

(a) For level  

99.5%

and sample size  

6

(b) For level  

95%

and sample size  

15

(c) For level  

80%

and sample size  

29

(d) For level  

98%

and sample size  

12

Answer 1

solution

Degrees of freedom = df = n - 1 = 6- 1 = 5

At 95.5% confidence level the t is ,

= 1 - 99.5% = 1 - 0.995 = 0.005

  / 2= 0.005 / 2 = 0.0025

t /2,df = t0.0025,5 = 4.772 ( using student t table)

b.

n = Degrees of freedom = df = n - 1 =15 - 1 = 14

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,14 = 2.145 ( using student t table)

c.

n = Degrees of freedom = df = n - 1 =29 - 1 = 28

At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.80 = 0.20

  / 2= 0.20 / 2 = 0.10

t /2,df = t0.10,28 =1.313 ( using student t table)

d.

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

At 98% confidence level the t is

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

t /2,df = t0.01,11 = 2.718 ( using student t table)