Question

An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given set of hypotheses and T test statistic. Also determine if the null hypothesis would be rejected at LaTeX: \alphaα = 0.01. LaTeX: H_a: \mu > 0.5, n = 26, T = 2.485

Answer 1

The P-value is 0.01.

The null hypothesis is rejected.

Explanation:

If
`H_a: \mu>0.5`, then the null hypothesis is
`H_0: \mu\leq0.5`.

The significance level is 0.01.

The size of the sample is 26, so the degrees of freedom are 26-1=25.

`df=n-1=26-1=25`

The test statistic is T=2.485.

The P-value, for T=2.485 and df=25, can be looked up in a t-table.

The P-value is 0.01.

As the P-value is equal to the significance level, the effect is considered significant and the null hypothesis is rejected.