Question

1. When can you "accept" the null hypothesis to be true?
2. When you are writing the interpretation for a hypothesis test about the population mean and state that there is not enough evidence... Why or What do you use to make that determination?
3. When you are writing the interpretation for a hypothesis test about two population means and your claim is the null hypothesis, do you state to support or reject the claim?
4. Given the following interpretation, discuss what next steps the person making the claim may need to take, if any.

Based on our sample, at the 1% significance level, there is not enough evidence to support the car manufacturer's claim that the life of all car batteries is greater than 36 months.

Answer 1

The null hypothesis is the hypothesis set for plausible rejection. We either reject the null hypothesis or fail to reject it. We never accept the null hypothesis.

While writing the interpretation for a hypothesis test about the population mean , if it is stated that there is not enough evidence, we mean that there is not sufficient evidence to reject the null hypothesis and thus we fail to reject the null hypothesis at that level of significance.

While writing the interpretation for a hypothesis test about two population means and my claim is the null hypothesis, we reject the null hypothesis. Null hypothesis is always set up for plausible rejection.

Let the population mean life of all car batteries be denoted by

u

Here we are to test

H₀:
u
=36 against H₁:
u
>36

Then we compute the sample mean , sample size and sample SD, and consequently the test statistic is observed. Then obtain the p-value. If the p-vaue is less than 0.01, we reject the null hypothesis and if the p-value is more than 0.01, we fail to reject the null hypothesis. Make a conclusion according to that.

Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, give it a like. Thanks.