Decision Rule When using a P-Value
If P-value ≤ α, reject the null hypothesis.
If P-value >α, do not reject the null hypothesis.

When the population standard deviation is unknown and the sample size is less than 30, the z test is inappropriate for testing hypotheses involving means. A different test called the t test is used. The t test is used when σ is unknown and n<30.

t = x -μ over s/√n      d.f.=n-1

The formula for the t test is similar to the formula of the z test. But since the population standard deviation is unknown, the sample standard deviation is used instead.

Find the critical value for the following:

1. α = 0.05 with d.f = 16 for a right tailed test.
2. α = 0.01 with d.f = 22 for a left tailed test.
3. α = 0.10 with d.f = 18 for two tailed test.

Solution:

1. Find the 0.05 column in the top row and 16 in the left-hand column. Where the row and column meet, the appropriate critical value is found; +1.746.
2. -2.508 since the test is one-tailed test.
3. Find the 0.10 column in the row labeled "Two tails" and find 18 in the column labeled "d.f." The critical values are +1.734 and -1.734.

When testing hypotheses by using the t test (traditional method), follow the same procedure as to the z test, except use the Table F.


Posted by: V.E. Sabusap