Question

A scientist got a p-value of 0.039 when testing his data. Assuming there was a small difference between the means in the two groups of his hypothesis, will these results give a significant difference?

Answer 1

On this case since the
`p_v< \alpha` we have enough evidence to reject the null hypothesis at the significance level of 5%, and indeed that represent a significant result.

We need to remember that by general rule is
`p_v <\alpha` we can reject the null hypothesis (significant result), but is
`p_v >\alpha` we FAIL to reject the null hypothesis (not significant result), if we select another significance level the results would change if we use a significance level is different than 0.05

Explanation:

Assuming that the system of hypothesis are:

Null hypothesis:
`\mu_1 =\mu_2`

Alternative hypothesis:
`\mu_1 \\eq \mu_2`

And using a standard significance level assumed
`\alpha=0.05` who represent the typical value in order to test the hypothesis.

We know that after conduct the hypothesis test we got a p value of
`p_v =0.039`

On this case since the
`p_v< \alpha` we have enough evidence to reject the null hypothesis at the significance level of 5%, and indeed that represent a significant result.

We need to remember that by general rule is
`p_v <\alpha` we can reject the null hypothesis (significant result), but is
`p_v >\alpha` we FAIL to reject the null hypothesis (not significant result), if we select another significance level the results would change if we use a significance level is different than 0.05