In a study to see if there was an association between weight loss and the amount of a certain protein in a person€™s body fat, the researchers measured a number of different attributes in their 39 subjects at the beginning of the study. The article reported, €œThese subjects were clinically and ethnically heterogeneous.€ Two of the variables they measured were body mass index (BMI) and total cholesterol. The results are shown in the scatterplot along with the regression line.

a. What are the observational units in the study?
b. The equation of the least squares regression line for predicting total cholesterol from BMI is cholesterol = 162.56 ˆ’ 0.9658 (BMI). The following null distribution was created to test the association between people€™s total cholesterol number and their BMI using the slope as the statistic. The null and alternative hypotheses for this test can be written as: Null: No association between cholesterol and BMI in the population. Alt: Association between cholesterol and BMI in the population.

i. Based on information shown in the null distribution, how many standard deviations is our observed statistic below 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 a people€™s total cholesterol and their BMI? Explain.

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240 - 200- 160 120 20 40 50 60 BMI Total cholesterol O Correlation © Slope O t-statistic 200 Mean = 0.020 SD = 0.625 Num samples = 1000 150 100 50 -2 -1 0 3 Shuffled slopes Count 2.