The formula used to compute a confidence interval for the me

The formula used to compute a confidence interval for the mean of a normal population when n is small is the following. (xbar +/- (t critical value) s/square root of n) What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round the answers to two decimal places.)

(a) 98% confidence, n = 17

(b) 90% confidence, n = 11

(c) 99% confidence, n = 24

(d) 90% confidence, n = 23

(e) 95% confidence, n = 13

(f) 95% confidence, n = 8

Solution

using tables of T distribution

a)

alpha = 1 - 0.98 = 0.02/2 = 0.01

df = 17-1=16

critical values : 2.583

b)

1-0.90=0.1/2 = 0.05

df = 11-1=10

critical value =1.812

c)

1-0.99=0.01 / 2 = 0.005

df = 24-1=23

critical values = 2.807

d)

1-0.90 = 0.10 / 2 = 0.05

df = 23-1 = 22

critical value = 1.717

e)

1 - 0.95 = 0.05 / 2 = 0.025

df=12

critical values = 2.179

f)

1 - 0.95 = 0.05/2 = 0.025

df= 7

critical value = 2.365