Question

To study the effectiveness of possible treatments for insomnia, a sleep researcher
conducted a study with 12 participants. Four participants were instructed to count
sheep (the Sheep Condition), four were told to concentrate on their breathing (the
Breathing Condition), and four were not given any special instructions. Over the next
few days, measures were taken how long it took each participant to fall asleep. The
average times for the participants in the Sheep Condition were 14, 28, 27, and 31; for
those in the Breathing Condition, 25, 22, 17, and 14; and for those in the control
condition, 45, 33, 30, and 41. Do these results suggest that the different techniques have
different effects? Answer the question by conducting a hypothesis test at the 0.05
significant level.
Use the five steps of hypothesis testing and demonstrate your calculations.

Please demonstrate all calculations in detail in your answers including how you found the standard deviations. Thanks.

Answer 1

Summarizing sleep time in excel:

Sleep time condition wise
Sheep	Breathing	Control
14	25	45
28	22	33
27	17	30
31	14	41

This study requires ANOVA:

ANOVA output by excel:

SUMMARY
Groups	Count	Sum	Average	Variance
Sheep	4	100	25	56.66667
Breathing	4	78	19.5	24.33333
Control	4	149	37.25	48.25
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	660.5	2	330.25	7.665377	0.011387	4.256495
Within Groups	387.75	9	43.08333
Total	1048.25	11

Null hypothesis: different techniques doesn't have different effects

Alternate hypothesis: different techniques does have different effects

significant level. = 0.05

Our p-value from ANOVA = 0.011387 which is less than 0.05

Hence we reject Null hypothesis meaning different techniques does have different effects.

ANOVA calculations are quite complex and time consuming. Hence done via excel.