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∗t∗ for the given sample size and confidence level. Round critical t values to 3 decimal places.Sample size, n Confidence level Degree of Freedom Critical value, t∗t∗5 90 13 95 22 98 15 99

Answer 1

Answer and Step-by-step explanation: The critical value for a desired confidence level is the distance where you must go above and below the center of distribution to obtain an area of the desired level.

Each sample has a different degree of freedom and critical value.

To determine critical value:

1) Calculate degree of freedom: df = n - 1

2) Subtract the level per 100%;

3) Divide the result by 2 tails;

4) Use calculator or table to find the critical value t*;

For n = 5 Level = 90%:

df = 4

t = $\frac{1-0.9}{2}$ = 0.05

Using t-table:

t* = 2.132

n = 13 Level = 95%:

df = 12

t = $\frac{1-0.95}{2}$ = 0.025

Then:

t* = 2.160

n = 22 Level = 98%

df = 21

t = $\frac{1-0.98}{2}$ = 0.01

t* = 2.819

n = 15 Level = 99%

df = 14

t = $\frac{1-0.99}{2}$ = 0.005

t* = 2.977

The critical values and degree of freedom are:

sample size          level           df              critical value

     5                      90%           4                   2.132

   13                       95%            12                 2.160

   22                      98%            21                 2.819

   15                       99%            14                 2.977