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