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

Answer:

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

Step-by-step explanation:

Assuming that the system of hypothesis are:

Null hypothesis: $\mu_1 =\mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

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