How do you do this question?

This series diverges by the limit test (some books may call it the nth term test).

Recall the limit test is the idea if the sequence doesn't converge to 0, then the series diverges.

In this case, the sequence converges to n/(7n) = 1/7 since all we are about are the leading terms when n gets very large.

After some very large n value, we're effectively adding on 1/7 or very close to it, each time. The infinite sum does not approach a fixed value. It keeps growing forever.

Confidence interval: (21.9, 32.9).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 26 - 1 = 25

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 25 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.485

The margin of error is:

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 27.4 - 5.5 = 21.9 hours

The upper end of the interval is the sample mean added to M. So it is 27.4 + 5.5 = 32.9 hours

Confidence interval: (21.9, 32.9).