Using the t-distribution, it is found that since the <u>test statistic is greater than the critical value for the right-tailed test</u>, it is found that there is enough evidence to conclude that Battery B outlasts Battery A by more than 2 hours.
At the null hypothesis, it is <u>tested if it does not outlast by more than 2 hours</u>, that is, the subtraction is not more than 2:

At the alternative hypothesis, it is <u>tested if it outlasts by more than 2 hours</u>, that is:

- The sample means are:
- The standard deviations for the samples are

Hence, the standard errors are:

The distribution of the difference has <u>mean and standard deviation</u> given by:


The test statistic is given by:

In which
is the value tested at the hypothesis.
Hence:



The critical value for a <u>right-tailed test</u>, as we are testing if the subtraction is greater than a value, with a <u>0.05 significance level</u> and 12 + 12 - 2 = <u>22 df</u> is given by 
Since the <u>test statistic is greater than the critical value for the right-tailed test</u>, it is found that there is enough evidence to conclude that Battery B outlasts Battery A by more than 2 hours.
A similar problem is given at brainly.com/question/13873630