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 ?∗t∗ for the given sample size and confidence level. Round critical t values to 4 decimal places.

Sample size, n	Confidence level	Degree of Freedom	Critical value, ?∗t∗
4	90
6	95
26	98
18	99

Answer 1

SOLUTION:

Degrees of freedom = df = n - 1 = 4- 1 = 3

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,3 =2.353    ( using student t table)

B.

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

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,5 =2.571 ( using student t table)

C.

n = Degrees of freedom = df = n - 1 =26 - 1 = 25

At 98% confidence level the t is

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

t /2,df = t0.01,25 = 2.485 ( using student t table)

D.

Degrees of freedom = df = n - 1 = 18- 1 = 17

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,17 = 2.898    ( using student t table)