Question

Identify the critical t. An independent random sample is selected from an approximately normal population with unknown standard deviation. Find the degrees of freedom and the critical t value ?∗ for the given sample size and confidence level. Round critical t values to 4 decimal places.

Sample size, | Confidence level | Degree of Freedom | Critical value, ?∗

12 90 11 ???

9 95 8    ???

8 98 7 ???

3 99 2 ???

Help Entering Answers

Answer 1

Solution :

Given that,

a) sample size = n = 12

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

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t0.05,11 = 1.7959

b) sample size = n = 9

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

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,8 = 2.3060

c) sample size = n = 8

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

At 98% confidence level

= 1 - 98%

=1 - 0.98 =0.02

/2 = 0.01

t/2,df = t0.01,7 = 2.9980

d) sample size = n = 3

Degrees of freedom = df = n - 1 = 3 - 1 = 2

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t0.005,2 = 9.9248