Question

1. A researcher conducts a study on the effects of amount of sleep on creativity. Twenty subjects come to the researcher’s clinic. The researcher divides the subjects into four groups, each containing five subjects. Each group sleeps at the clinic for a different amount of time (2, 4, 6, or 8 hours). After awakening, each subject takes a test of creativity. The following table shows the creativity scores for the subjects in each group:

Amount of Sleep (in hours)
2	4	6	8
3	4	10	10
5	7	11	13
6	8	13	10
4	3	9	9
2	2	10	10

1. State the appropriate null and alternative hypotheses

2. Fill in the blanks in the following summary (source) table describing the results of the ANOVA:

Source	df	SS	MS	F
Between-groups		187.75
Within-groups
Total		242.95

3. Find the critical value of F. Assume a level of significance of .05.

4. Based on the results of the ANOVA, what is the correct conclusion regarding the null hypothesis?

5. What does this result mean in terms of the alternative hypothesis?

6. Should you perform a post hoc test in this case? Explain why or why not. What information does the post hoc test provide?

7. Conduct a Tukey’s HSD test to test the differences between all possible pairs of sample means at the .05 level of significance and complete the following table.

Comparison	X-X	Q
2hrs – 4hrs
2hrs – 6hrs
2hrs – 8hrs
4hrs – 6hrs
4hrs – 8hrs
6hrs – 8hrs

8. What is the value of Q_CRIT?

1. Which pairs of sample means are significantly different?

Answer 1

Ho: µ1=µ2=µ3=µ4
H1: not all means are equal

	SS	df	MS	F	p-value	F-critical
Between:	187.75	3	62.58	18.14	0.0000	3.24
Within:	55.20	16	3.45
Total:	242.95	19

F-critical

3.24

F stat > f critical , reject Ho

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mean of all groups are not same

...............

yes we should post hoc test . because means are different

and pot hoc test tell us which means are different and which are not

.......................

Level of significance	0.05
no. of treatments,k	4
DF error =N-k=	16
MSE	3.450
q-statistic value(α,k,N-k)	4.0500

critical value = q*√(MSE/n)

			confidence interval
population mean difference	critical value	lower limit	upper limit	result
µ1-µ2	-0.80	3.36	-4.16	2.56	means are not different
µ1-µ3	-6.60	3.36	-9.96	-3.24	means are different
µ1-µ4	-6.40	3.36	-9.76	-3.04	means are different
µ2-µ3	-5.80	3.36	-9.16	-2.44	means are different
µ2-µ4	-5.60	3.36	-8.96	-2.24	means are different
µ3-µ4	0.20	3.36	-3.16	3.56	means are not different

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Please revert back in case of any doubt.

Please upvote. Thanks in advance.