"To Breakfast or Not to Breakfast?" by Richard Ayore

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. Though not sure, my brother insisted that it was more than two hours. Using the data in Table 10.29, solve our problem.

$\begin{array}{|ll|}\hline \text{Work hours with breakfast}& \text{Work hours without breakfast}\\ 8& 6\\ 7& 5\\ 9& 5\\ 5& 4\\ 9& 7\\ 8& 7\\ 10& 7\\ 7& 5\\ 6& 6\\ 9& 5\\ \hline\end{array}$

Step by step solution

01

Given Information 

Given in the question that,

$\begin{array}{|ll|}\hline \text{Work hours with breakfast}& \text{Work hours without breakfast}\\ 8& 6\\ 7& 5\\ 9& 5\\ 5& 4\\ 9& 7\\ 8& 7\\ 10& 7\\ 7& 5\\ 6& 6\\ 9& 5\\ \hline\end{array}$

02

Explanation 

a. The null hypothesis is defined as follows:

$H_0:{\mu }_d=0$

b. The following is an alternative hypothesis:

$H_0:{\mu }_d>0$

c. The random variable $X_d$represents the mean difference between working days when breakfast is eaten and working days when breakfast is not eaten.

d. The distribution of students.

e. Fill in all requirements using Minitab's two sample t test option.

the result will be:

The value of test statistics: $5.16$

f. From the output, the $p$value is: $0.000$

g. Because the value of $p$is $0.000$, there is no need for a graph.

$\alpha =0.05$

The null hypothesis must be rejected.

$p$value is less than$\alpha$is the reason for the decision.

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