Question

What critical value t* from Table C would you use for a confidence interval for the mean of the population in each of the following situations? (Use 3 decimal places.)
(a) A 95% confidence interval based on n = 15 observations.

t* =

(b) A 99% confidence interval from an SRS of 29 observations.

t* =
(c) A 80% confidence interval from a sample of size 9.
t* =

Answer 1

Solution,

a) sample size = n = 15

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

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t_0.025,14 = 2.145

b) sample size = n = 29

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

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t_0.005,28 = 2.763

c) sample size = n = 9

degrees of freedom = df = n - 1 = 9 - 1 = 8

At 80% confidence level

= 1 - 80%

=1 - 0.80 =0.20

/2 = 0.10

t/2,df = t_0.10,8 = 1.397