Question

G two samples, one of size 14 and the second of size 13, are selected to test the difference between two population means. how many degrees of freedom are used to find the critical value? assume the population standard deviations are equal.

Answer 1

Note :- If sample size n > 30 OR Population standard deviation σ is given then We use Z test.

If sample size n < 30 AND Population standard deviation σ is unknown then we use t test.

In this question we are not given Population standard deviations σ1 and σ2.

Also n1 = 14 and n2 = 13 both sample sizes are LESS than 30.

Therefore we use t test.

Given :- Assume the population standard deviations are equal. ( σ1 = σ2)

then Degrees of freedom = n1 + n2 - 2 = 14 + 13 - 2 = 25.

(kindly find the image attached with this solution)

Answer :- Therefore 25 degrees of freedom are used to find the t critical value.