If n1= 22 and n2=15 what critical value would you use to test the claim μ1<μ when α=.05​?

Question

If n1= 22 and n2=15 what critical value would you use to test the claim μ1<μ when α=.05​?

Answer 1

The answer depends on the agreement how to calculate df for t-distribution.

In some textbooks (like Triola) there is suggested a simple way: df = n₁ + n₂ - 2 = 22+15-2 = 35

Then the critical value would be -1.69 (this is left-tailed test).

However, for many resources (TI-83/84, https://www.wolframalpha.com and others) is implemented more accurate way of calculating df. The formula of df uses not only the sample sizes n1 and n2, but also the sample standard deviations s1 and s2.

Without values s1 and s2 we cannot find the critical value.