Question

Use the following information to run a t-Test in excel. 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

Use the following information to run a t-Test in excel. 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?

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.

Descriptive statistics
	Work hours with breakfast	Work hours without breakfast
n	10	10
mean	7.8000	5.7000
sample standard deviation	1.5492	1.0593
sample variance	2.4000	1.1222

Since data are paired, Paired t test used

This is an upper tail test

= 0.2458

DF = n-1 =9

Table value of t with 9 DF at 0.05 level =1.8331

Rejection Region: Reject Ho if or t > 1.8331

Calculated t =0.2458 , not in the rejection region

The null hypothesis is not rejected.

It is not statistically significant.

There is not enough evidence to conclude that it work more than two hours when take breakfast.

Paired t Test
Data
Hypothesized Mean Difference	2
Level of significance	0.05
Intermediate Calculations
Sample Size	10
DBar	2.1000
Degrees of Freedom	9
SD	1.2867
Standard Error	0.4069
t Test Statistic	0.2458
Upper-Tail Test
Upper Critical Value	1.8331
p-Value	0.4057
Do not reject the null hypothesis