Question

Use the following information to run a t-Test. Write a paragraph description about the information you found and the conclusions you can draw

Your write up should discuss all aspects of hypothesis testing, what is your null and alternative, what are the means and variances of each group, are we running a one- or two-tailed test, why? What is the test statistic, is it statistically significant?

In the American society, birthdays are one of those days that everyone looks forward to. People of different ages and peer groups gather to mark the 18th, 20th, …, birthdays. During this time, one looks back to see what he or she has achieved for the past year and also focuses ahead for more to come.

If, by any chance, I am invited to one of these parties, my experience is always different. Instead of dancing around with my friends while the music is booming, I get carried away by memories of my family back home in Kenya. I remember the good times I had with my brothers and sister while we did our daily routine.

Every morning, I remember we went to the shamba (garden) to weed our crops. I remember one day arguing with my brother as to why he always remained behind just to join us an hour later. In his defense, he said that he preferred waiting for breakfast before he came to weed. He said, “This is why I always work more hours than you guys!”

And so, to prove him wrong or right, we decided to give it a try. One day we went to work as usual without breakfast, and recorded the time we could work before getting tired and stopping. On the next day, we all ate breakfast before going to work. We recorded how long we worked again before getting tired and stopping. Of interest was our mean increase in work time. My brother insisted that it was more than two hours.

Work hours with breakfast	Work hours without breakfast
8	6
7	5
9	5
5	4
9	7
8	7
10	7
7	5
6	6
9	5

Answer 1

Let denote the mean work hours with and without breakfast respectively.

To test: Vs (One sided test)

First, computing the sample means and standard deviations of the two groups:

Similarly,

Assuming that the population variation are equal, the test statistic is given by:

= 3.538

The critical region of the one tailed test is given by t> t_18,0.05

Comparing the test statistic with critical value of t for 10 + 10 - 2 = 18 df, at 5% significance level:

Since, t = 3.538> 1.734, our test statistic lies in the critical / rejection region.We may reject H₀ at 5% level.The test is statistically significant.

We may thus, conclude that the brother's claim that mean increase in work time after breakfast was more than 2 hours is true, based on this data.