Question

A sleep researcher conducted a study where 4 participants were instructed to count sheep and 4 were told to concentrate on their breathing and 4 were not given any special instruction. The average number of minutes taken for each participants to fall asleep over the next 7 days were 14, 18, 27, 31 minutes for the sheep counters. 25, 22, 17, 14 minutes for the breathing ones, and 45, 33, 30, and 41 for the control condition. using the .05 significance level what is the value of the Grand mean? What is the F ratio? What is the final F value? Is the F value extreme enough to reject the null hypothesis?

Answer 1

The output of one-way ANOVA analysis is

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Counting	4	90	22.5	61.66667
Breathing	4	78	19.5	24.33333
None	4	149	37.25	48.25
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	722.1667	2	361.0833	8.068901	0.009831	4.256495
Within Groups	402.75	9	44.75
Total	1124.917	11

F-ratio = 8.0689

Yes reject the null hypothesis.