Student researchers asked their subjects how much sleep they had the previous night (in hours) and then timed how long it took them (in seconds) to complete a paper and pencil maze. The results are shown in the scatterplot along with the regression line.

a. What is the explanatory variable?
b. What is the response variable?
c. The equation of the least squares regression line for predicting price from number of pages is time = 190.33 ˆ’ 7.76 (sleep). The following null distribution was created to test the association between time to complete maze and amount of sleep using the slope as the statistic. The null and alternative hypotheses for this test can be written as: Null: No association between sleep and time in the population. Alt: Association between sleep and time in the population.

i. Based on information shown in the null distribution, how many standard deviations is our observed statistic away from the mean of the null distribution? (That is, what is the standardized statistic?)
ii. Based on your standardized statistic, do you have strong evidence of an association between the time it takes someone to complete the maze and how much sleep they got the night before? Explain.

Transcribed Image Text:

360 270 180 90 6. 10 Sleep Time Mean = 0.202 200 SD = 7.556 Num samples = 1000 150 100 50 -30 -20 -10 0 10 20 Shuffled slopes Count