Question

Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means. State the degrees of freedom used.

Find the endpoints of the t-distribution with 2.5% beyond them in each tail if the samples have sizes n1=16 and n2=23.

Enter the exact answer for the degrees of freedom and round your answer for the endpoints to two decimal places

Answer 1

Solution:

Given:

Sample sizes: n₁= 16 , n₂ = 23

We have to find  the endpoints of the t-distribution with 2.5% beyond them in each tail.

thus two tail area = 2.5%+2.5% = 5% = 0.05

degrees of freedom = n₁+ n₂   - 2

degrees of freedom =   16 + 23 - 2

degrees of freedom = 37

Use following excel command:

=T.INV.2T(probability, degree_freedom)

=T.INV.2T(0.05,37)

=2.0261925

=2.03

thus  the endpoints of the t-distribution are: ( -2.03 , 2.03 )

or it can be written as: