Participant	Sleep Time	Reaction Time
1	7	0.08
2	8.5	0.08
3	8	0.09
4	7	0.17
5	6.5	0.09
6	5	0.16
7	7.25	0.09
8	7	0.08
9	8.5	0.06
10	8	0.06
11	4	0.22
12	7	0.15
13	5	0.18
14	5	0.15
15	8.5	0.07
16	7	0.09
17	6.5	0.09
18	7	0.07
19	6	0.17
20	4.5	0.19

As a consumer of research, you know that relationships are of critical importance. You must first know if a relationship exists between two variables before you can determine if one variable may account for another. In this week's Learning Resources, you learned about correlations, which are used to determine if two variables are related to one another. You also learned that you cannot infer causation from a significant correlation alone. For example, you might find that years of education and salary are related, but that does not tell you if more education causes your salary to increase. In correlational studies, you cannot show that one variable causes a change in another variable. To determine causation, an experimental design is needed. However, correlations can demonstrate that as one variable increases, another tends to increase as well (positive relationship). You also may find that as one variable increases, the other tends to decrease (negative relationship). You may even find that there is no relationship at all between variables.

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. You can find the data for this Assignment in the Weekly Data Set forum found in the Discussions area of the course navigation menu.

1. Before computing the correlation, state the null hypothesis and alternative hypothesis in words (not formulas).
2. Based on the hypotheses you stated, explain whether the researcher should conduct a one-tailed or two-tailed test.
3. Identify the correlation coefficient (r) for this data set using SPSS and report it in your answer document.
4. State the degrees of freedom and explain how you calculated it by hand.
5. Identify the p value using SPSS and report it in your answer document.
6. Explain whether the researcher should retain or reject the null hypothesis.
7. Are the results statistically significant? Explain how you know.
8. Explain what the researcher can conclude about the relationship between amount of sleep and reaction times. Include a description of the direction (positive, negative, or no relationship) and strength (weak, moderate, or strong) of the relationship.