Question

1. Assume the computed t-statistic was t0=1.987

   1. Find the t-critical value for a one-tailed test at the 0.05 significance level with 19

      degrees of freedom. Is there sufficient evidence to reject the null hypothesis?

   2. Find the t-critical value for a one-tailed test at the 0.05 significance level with a sample

      size of 30. Is there sufficient evidence to reject the null hypothesis?

   3. Find the t-critical value for a two-tailed test at the 0.05 significance level with 15

      degrees of freedom. Is there sufficient evidence to reject the null hypothesis?

   4. Find the t-critical value for a two-tailed test at the 0.05 significance level with a sample

      size of 26. Is there sufficient evidence to reject the null hypothesis?

Answer 1

Part a)

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 20-1) = 1.729
t > t(α, n-1) = 1.987 > 1.729
Result :- Reject null hypothesis

Part b)

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 30-1) = 1.699
t > t(α, n-1) = 1.987 > 1.699
Result :- Reject null hypothesis

Part c)

Test Criteria :-
Reject null hypothesis if | t | > t(α/2, n-1)
Critical value t(α/2, n-1) = t(0.05 /2, 16-1) = 2.131
| t | > t(α/2, n-1) = 1.987 < 2.131
Result :- Fail to reject null hypothesis

Part d)

Test Criteria :-
Reject null hypothesis if | t | > t(α/2, n-1)
Critical value t(α/2, n-1) = t(0.05 /2, 26-1) = 2.060
| t | > t(α/2, n-1) = 1.987 < 2.06
Result :- Fail to reject null hypothesis