For a hypothesis comparing two population means, h0: μ1 ≤ μ2, what is the critical value for a one-tailed hypothesis test, using a 5% significance level, with both sample sizes equal to 13? assume the population standard deviations are equal. g

We know about hypothesis that,

H0:- µ1 ≤ µ2 VS Ha :- µ1 > µ2.

Note :- If Ha has > sign then test is Right tailed (one tailed ).

If Ha has < sign then test is left tailed (one tailed )

If Ha has ≠ sign then we say that the test is two tailed.

Therefore the test is right tailed test.

Given :- both sample sizes equal to 13. That is, n1 = 13 and n2 = 13.

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.

Both sample sizes are 13 which are less than 30 so we use t test.

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

Degrees of Freedom = n1 + n2 - 2 = 13 + 13 -2 = 24.

Level of signficance = α = 0.05.

By using the t table attached here , Look for the corresponding t critical value for df = 24 and α = 0.05 in one tailed area.

t critical = 1.711.