Question

What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.)

(a) 90% confidence, n = 17


(b) 90% confidence, n = 12


(c) 99% confidence, n = 24


(d) 90% confidence, n = 23


(e) 80% confidence, n = 13


(f) 95% confidence, n = 9

Answer 1

Answer:

(a) the critical value of t at P = 10% and 16 degrees of freedom is 1.337.

(b) the critical value of t at P = 10% and 11 degrees of freedom is 1.363.

(c) the critical value of t at P = 1% and 23 degrees of freedom is 2.500.

(d) the critical value of t at P = 10% and 22 degrees of freedom is 1.321.

(e) the critical value of t at P = 20% and 12 degrees of freedom is 0.8726.

(f) the critical value of t at P = 5% and 8 degrees of freedom is 1.860.

Step-by-step explanation:

We have to find the critical t value for each of the following confidence levels and sample sizes given below.

As we know that in the t table there are two columns. The horizontal column is represented by the symbol P which represents the level of significance and the vertical column is represented by the symbol '$\nu$' which represents the degrees of freedom.

(a) So, here the level of significance = 1 - confidence level

                                                            = 1 - 0.90 = 0.10

And the degrees of freedom = n - 1

                                                = 17 - 1 = 16

Now, in the t table, the critical value of t at P = 10% and 16 degrees of freedom is 1.337.

(b) So, here the level of significance = 1 - confidence level

                                                            = 1 - 0.90 = 0.10

And the degrees of freedom = n - 1

                                                = 12 - 1 = 11

Now, in the t table, the critical value of t at P = 10% and 11 degrees of freedom is 1.363.

(c) So, here the level of significance = 1 - confidence level

                                                            = 1 - 0.99 = 0.01

And the degrees of freedom = n - 1

                                                = 24 - 1 = 23

Now, in the t table, the critical value of t at P = 1% and 23 degrees of freedom is 2.500.

(d) So, here the level of significance = 1 - confidence level

                                                            = 1 - 0.90 = 0.10

And the degrees of freedom = n - 1

                                                = 23 - 1 = 22

Now, in the t table, the critical value of t at P = 10% and 22 degrees of freedom is 1.321.

(e) So, here the level of significance = 1 - confidence level

                                                            = 1 - 0.80 = 0.20

And the degrees of freedom = n - 1

                                                = 13 - 1 = 12

Now, in the t table, the critical value of t at P = 20% and 12 degrees of freedom is 0.8726.

(f) So, here the level of significance = 1 - confidence level

                                                            = 1 - 0.95 = 0.05

And the degrees of freedom = n - 1

                                                = 9 - 1 = 8

Now, in the t table, the critical value of t at P = 5% and 8 degrees of freedom is 1.860.