In: Math

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.

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.

Problem:
To study the effectiveness of possible treatments for
insomnia, a sleep researcher conducted a study in which 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. The
average number of minutes taken for each participant to fall asleep
over the next seven days were 14, 28, 27, and 31 minutes for the
Sheep condition; 25, 22, 17, and 14...

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