Question

Recall the researcher who investigated the relationship between hours of sleep and reaction times in the Week 4 Application. As a follow up to that study, the researcher wants to conduct a correlation to investigate further if there is a relationship between hours of sleep and reaction time. For this experiment, participants are allowed to sleep as much as they would like (that is, they are not assigned to sleep any specific number of hours). When 20 participants come to their appointment time, they report to the researcher how many hours of sleep they had the previous night. The researcher then tests their reaction times.

data:

Participant	Sleep Time	Reaction Time
1	6	0.23
2	8.5	0.21
3	6.5	0.23
4	7	0.24
5	6	0.3
6	7	0.23
7	8.5	0.22
8	7.25	0.23
9	6.75	0.29
10	6.25	0.31
11	6.25	0.29
12	7	0.25
13	6.75	0.29
14	8	0.22
15	7.75	0.21
16	7.25	0.28
17	6.75	0.23
18	6.25	0.3
19	7.75	0.22
20	7.25	0.21

Answer 1

Recall the researcher who investigated the relationship between hours of sleep and reaction times in the Week 4 Application. As a follow up to that study, the researcher wants to conduct a correlation to investigate further if there is a relationship between hours of sleep and reaction time. For this experiment, participants are allowed to sleep as much as they would like (that is, they are not assigned to sleep any specific number of hours). When 20 participants come to their appointment time, they report to the researcher how many hours of sleep they had the previous night. The researcher then tests their reaction times.

Excel used for correlation:

Correlation Matrix
		Sleep Time	Reaction Time
	Sleep Time	1.0000	-0.6701
	Reaction Time	-0.6701	1.0000
		20	sample size
		± .444	critical value .05 (two-tail)
		± .561	critical value .01 (two-tail)

Correlation between hours of sleep and reaction time = -0.6701

Test for significance of Correlation

t= -3.8301

DF = n-2 =18

Table value of t with 18 DF at 0.05 level =2.101

Rejection Region : Reject Ho if t < -2.101 or t > 2.101

Calculated t = -3.8301 falls in the rejection region.

The null hypothesis is rejected.

We conclude that Correlation between hours of sleep and reaction time is significant and negative. If hours of sleep increases the reaction time decreases.