Question

(Please answer step-by-step. Typed work preferable.)

1. Your hapless statistics professor and the National Association of Pillow-makers (NAP) have asked you to investigate the insidious impact of caffeine consumption on student-professor relations. To study the topic you collect the following information about the number of cups of coffee consumed by a sample of students in a given day during finals week and the number of violent thoughts they have about their professors.

Student #	Cups of Coffee	Violent Thoughts
1	6	5
2	3	2
3	2	8
4	4	9
5	3	3
6	0	1
7	1	4
8	5	6
9	7	7
10	4	0

a. With a single statistic, summarize the strength and the direction of the association between the number of cups of coffee consumed and the number of violent thoughts for this group of students. Be sure to name and interpret the statistic you use.

b. Do your data provide enough evidence to conclude that the association between coffee consumption and violent thoughts exists in the population from which your sample was drawn? (Again, you will need to perform a hypothesis test.) Explain your answer and show all necessary work. You should write out the research and null hypotheses in Greek notation.

Answer 1

a. With a single statistic, summarize the strength and the direction of the association between the number of cups of coffee consumed and the number of violent thoughts for this group of students. Be sure to name and interpret the statistic you use.

Student #	Cups of Coffee x	Violent Thoughts y	x*x	y*y	x*y
1	6	5	36	25	30
2	3	2	9	4	6
3	2	8	4	64	16
4	4	9	16	81	36
5	3	3	9	9	9
6	0	1	0	1	0
7	1	4	1	16	4
8	5	6	25	36	30
9	7	7	49	49	49
10	4	0	16	0	0
Total	35	45	165	285	180

Pearson Correlation coefficient is used.

= 0.380

Correlation coefficient is 0.380. There is positive association between the number of cups of coffee consumed and the number of violent thoughts.

b. Do your data provide enough evidence to conclude that the association between coffee consumption and violent thoughts exists in the population from which your sample was drawn? (Again, you will need to perform a hypothesis test.) Explain your answer and show all necessary work. You should write out the research and null hypotheses in Greek notation.

t=1.162

DF =10-2 =8

Table value of t with 8 DF at 0.05 level =2.306

Calculated t =1.162 < 2.306 , the table value

The null hypothesis is not rejected.

We conclude that there is no significant association between the number of cups of coffee consumed and the number of violent thoughts.