Question

Use the following information to run a t-Test. Give a description about the information you found and the conclusions you can draw. Should include the following at minimum; the null and alternative hypothesis, mean and variances the two groups, the test(s) you are running and why, the test statistic and the critical value, and what conclusions do we draw, do we reject the null or accept the null.

"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 half of us went to work as usual without breakfast, and recorded the time we could work before getting tired and stopping. The other half all ate breakfast before going to work, and recorded how long they worked again before getting tired and stopping. My brother insisted that there would be an increase of 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

Ho :   µ1 - µ2 =   2                  
Ha :   µ1-µ2 >   2                  
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   sample 1                  
mean of sample 1,    x̅1=   7.80                  
standard deviation of sample 1,   s1 =    1.55                  
size of sample 1,    n1=   10                  
                          
Sample #2   ---->   sample 2                  
mean of sample 2,    x̅2=   5.70                  
standard deviation of sample 2,   s2 =    1.06                  
size of sample 2,    n2=   10                  
                          
difference in sample means =    x̅1-x̅2 =    7.8000   -   5.7   =   2.10  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    1.3271                  
std error , SE =    Sp*√(1/n1+1/n2) =    0.5935                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   2.1000   -   2   ) /    0.59   =   0.168
                          
Degree of freedom, DF=   n1+n2-2 =    18                  

p-value =        0.434036   [excel function: =T.DIST.RT(t stat,df) ]              
Conclusion:     p-value>α , Do not reject null hypothesis                      

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THANKS

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