Question

Find the critical value for a​ right-tailed test with alpha equals 0.01​, degrees of freedom in the n=12​, and degrees of freedom in the degrees of freedom=50.

Answer 1

You draw these critical values from the Student’s t-distribution with n – 1 degrees of freedom (df).

For testing hypotheses about the population mean, the appropriate number of degrees of freedom is one less than the sample size (that is, n – 1).

The critical value or values are used to locate the area under the curve of a distribution that is too extreme to be consistent with the null hypothesis. For a right-tailed test, these are the large positive values, which are collectively known as the right tail of the distribution. The area in the tail equals the level of significance of the hypothesis test

for a right tailed test,

=> level of significance is 0.01 and the sample size is 12; then you get a single positive critical value:

t_α, n -1 =t_0.01,11

It can be shown using either statistical software or a t-table that the critical value t _0.01,11 is 2.718.

=> level of significance is 0.01 and the sample size is 50; then you get a single positive critical value:

t_α, n -1 =t_0.01,49

It can be shown using either statistical software or a t-table that the critical value t _0.01,49 is 2.405..