Question

When we get a p-value that is very large, we may conclude that:

A) The null hypothesis has been proven to be true

B) There is strong evidence for the alternative hypothesis

C) The null hypothesis is plausible

D) The alternative hypothesis has been proven to be false.

Answer 1

C) The null hypothesis is plausible

Explanation:

1) Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

2) Solution to the problem

The p value is a meaasure in order to take a decision respect the null hypothesis.

If
`p_v <\alpha` we reject the null hypotheis at the significance level
`\alpha`.

If
`p_v > \alpha` we FAIL to reject the null hypotheis at the significance level
`\alpha`.

So on this case if we got a p value very large we can conclude that the null hypothesis is plausible.

A) The null hypothesis has been proven to be true

False. We don't know if the null hypothesis is true at all since we have a significance level
`\alpha`

B) There is strong evidence for the alternative hypothesis

False, if the p value is large we FAIL to reject the nul hypothesis. So then we can't decide in favour of the alternative hypothesis.

C) The null hypothesis is plausible

Correct thats the best option based on the statistical evidence.

D) The alternative hypothesis has been proven to be false.

No since we have a significance level and probability of commit error type I or II. So we can conclude that one hypothesis is at all true or false.