The onesample t statistic from a sample of n 5 observations

The one-sample t statistic from a sample of n = 5 observations for the two-sided test of

H₀: ? = 50
H_a: ? ? 50

has the value t = 2.50.

Step 1:
What are the degrees of freedom for t?

Step 2:
Is the value t = 2.50 statistically significant at the 10% level? At the 5% level?

Solution

Step 1: The degrees of freedom for the t-test is 4.

Step 2: The quantiles of the t-distribution with 4 degrees of freedom at 10% and 5% level of significance are respectively 2.13 and 2.78. Since t=2.5 is greater than 2.13 but less than 2.78, the value t = 2.50 is significant at the 10% level, but not at the 5% level