A 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.

Use SPSS to determine if amount of sleep is related to reaction time.

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.

Data Set:

ParticipantSleep TimeReaction Time

1 6.5 0.26

2 7.5 0.22

3 6.5 0.27

4 7 0.29

5 7.5 0.22

6 7 0.28

7 8.5 0.2

8 7.25 0.3

9 6.75 0.28

10 6.25 0.24

11 6 0.3

12 6.5 0.28

13 7 0.29

14 6.25 0.27

15 7 0.29

16 8.5 0.22

17 7.25 0.29

18 8 0.21

19 7.25 0.22

20 6 0.24