Question

Question 28 options:

You want to know what is the optimal amount of sleep to maximize cognitive performance. You conduct a study in which 4 participants are randomly assigned to each of 4 conditions. The condition differ only in how many hours of sleep they receive per night. You install an app on the participants’ phones which wakes them up every morning after the prescribed number of hours of sleep. After two weeks, you give all of the participants a spatial reasoning test which has been shown to correlate strongly with overall cognitive ability. The table below shows the resulting data. Conduct a hypothesis test to determine if there is a significant difference in performance across the conditions.

4 hours per night	6 hours per night	8 hours per night	10 hours per night
80	50	100	90
50	90	60	50
30	60	30	20
10	20	70	60

Enter the result for each step below:

State the null hypothesis (just the null, no need to state the alternative; for μ₁ simply type "mu1"):

Enter the F-value that marks the boundary of the positive critical region under the null hypothesis (hint, if you drew out the distribution, the boundary marks the beginning of the shaded area on the right side) (enter a number with 2(TWO) decimal places using only the keys "0-9" and "." DO NOT TYPE ANY LETTERS OR SPACES):

What is the Sum of Squares Between (enter a number with 2(TWO) decimal places using only the keys "0-9" and "." DO NOT TYPE ANY LETTERS OR SPACES)?

What is the Sum of Squares Within (enter a number with 2(TWO) decimal places using only the keys "0-9" and "." DO NOT TYPE ANY LETTERS OR SPACES)?

What is the Mean Square (MS) Between (enter a number with 2(TWO) decimal places using only the keys "0-9" and "." DO NOT TYPE ANY LETTERS OR SPACES)?

What is the Mean Square (MS) Within (enter a number with 2(TWO) decimal places using only the keys "0-9" and "." DO NOT TYPE ANY LETTERS OR SPACES)?

What is the the F-ratio (enter a number with 2(TWO) decimal places using only the keys "0-9" and "." DO NOT TYPE ANY LETTERS OR SPACES)?

Do you reject the null hypothesis (type yes or no):

Answer 1