Question

Dr. Kovaleski is interested in examining whether quantity of sleep impacts problem solving ability. To test problem solving ability, the research team gave participants a puzzle and measured how long it took participants to solve the puzzle in minutes. A group of participants were instructed to sleep 5 hours and then solve the puzzle in the morning. Then the same participants were instructed to sleep 7 hours and then solve a different puzzle in the morning. Then, participants were asked to sleep 9 hours and then solved a third puzzle in the morning.

5 hours	7 hours	9 hours
6	4	6
8	3	1
9	5	3
6	6	6
5	2	1

Answer the following questions and compute the Repeated Measures One Way ANOVA for the data provided above. For this example, assume that alpha is 0.05.

1. What is the research question?

Answer 1

Using Excel, go to Data, select Data Analysis, choose Anova: Single Factor at alpha = 0.05

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	32.93	2	16.47	4.30	0.039	3.89
Within Groups	46.00	12	3.83
Total	78.93	14

Research question: Does quantity of sleep impact problem solving ability?

H₀: μ₁ = μ₂ = μ₃, There is no difference in time taken to solve puzzle after sleeping for 5 hours, 7 hours or 9 hours

H₁: At least one μ_i is different, There is a difference in time taken to solve puzzle after sleeping for 5 hours, 7 hours or 9 hours.

p-value = 0.039

Level of significance = 0.05

Since p-value is lessthan 0.05, we reject the null hypothesis and conclude that at least one μ_i is different.

So, there is a difference in time taken to solve puzzle after sleeping for 5 hours, 7 hours or 9 hours. Hence, quantity of sleep impacts problem solving ability.