Question

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

Answer 1

For n1=22, the degrees of freedom (DOF)=21 and for n2=15, DOF=14. We are specifically testing μ1<μ, where μ1 is presumably the sample mean for each sample, or their average. This is a one-tailed t-test, with the significance level α=0.05, a confidence level of 95%. (A 2-tailed test would apply if we were testing μ1≠μ, which is an "either side"-of-the-mean test. We are only interested in the left-side of the mean, hence a 1-tailed test.)

The individual critical values from tables would be 1.761 (DOF=14) and 1.721 (DOF=21).

The combined DOF is 22+15-2=35 or the sum of the individual DOFs=21+14=35. This gives us a critical value of 1.691 approx.

Comments

that what I got too but it's still not right. That why I posted the question not sure what I'm doing wrong. Here a screen shot of the question just in case I fat fingered something - thanks

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I wasn’t clear whether the question required two answers or one, but from your comment it would appear that the two samples were to be combined, so that means effectively we have a combined dataset with 37 elements. So in theory the DOF could be 1 less than this. In practice, though, it’s customary to combine the separate DOFs. Another possible reason for the discrepancy is that a dataset with more than 30 elements could be considered large enough to constitute a normal distribution, so the Z critical value could be used. Most t tables don’t list 35 (or 36) DOF, so the value has to be interpolated.