Question

In: Statistics and Probability

3. Determine the critical value of t in each of the following circumstances: a. 1 −...

3. Determine the critical value of t in each of the following circumstances: a. 1 − α = 0.95, n=15

b. 1 − α = 0.99, n=20

c. 1 − α = 0.90, n=40

Solutions

Expert Solution

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)

b.

Degrees of freedom = df = n - 1 = 20 - 1 = 19

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,19 = 2.861 ( using student t table)

c.

Degrees of freedom = df = n - 1 =40  - 1 = 39

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,39 = 1.685 ( using student t table)

orchestra answered 2 years ago
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