Question 1. A random sample of 1001 University of California faculty members taken in December 1995 was asked, "Do you favor or oppose using race, religion, sex, color, ethnicity or national origin as a criterion for admission to the University of California?" (Roper Center, 1996). 52% responded "favor".
a. What is the population for this survey?
b. What is the sample?
c. What is the variable of interest?
Question 2. For each of the following, decide whether it is an observational study or a randomized experiment? If it is an experiment, give the explanatory and response variables.
a. A group of 100 students was randomly divided, with 50 assigned to receive vitamin C, and the remaining 50 to receive a placebo, to see if vitamin C helps prevent colds.
b. All patients who underwent hip replacement surgery at Stanford University Hospital during 1990 to 2000 will be followed for 10 years after their operation to determine the success (or failure) of the replacement.
c. A group of students who were enrolled in an Introductory Statistics course were randomly assigned to take a Web-based course or to take a traditional lecture course.
The two methods were compared by giving the same final examinations in both courses.
d. A group of smokers and another group of nonsmokers who visited a particular clinic were asked to come in for a physical exam every 5 years for the rest of their lives in order to monitor and compare their health status.
Question 3. A fast food chain sells its burgers alone or as part of a "value meal" which includes fries and a drink. They know some customers are health conscious. They want to do an experiment to see if the proportion of customers choosing the meal would increase if they offered baby carrots with the meal as an alternative to the fries. They will compare three treatments: (1) status quo, (2) offering carrots as an alternative, but with no advertising, and
(3) offering carrots as an alternative, and advertising this option in the local area.
What are the explanatory and response variables?
b. Diagram the experiment.
Question 4. Many studies have been done that that indicate that the maximum heart rate an individual can reach during intensive exercise decreases with age. A physician decided to do his own study and recorded the ages and peak heart rates of 10 randomly selected people. The results are shown in the following table, wherex denotes age, in years, and y denotes peak heart rate.
-------------------------------------------------------------------------------------------------
X 30 38 41 38 29 39 46 41 42 24
-------------------------------------------------------------------------------------------------
Y 186 183 171 177 191 177 175 176 171 196
------------------------------------------------------------------------------------------------
Using the following computer generated output:
a. Determine the equation of the line of regression.
b. Describe the apparent relationship between age and peak heart rate.
c. What does the slope of the regression line represent in terms of age and peak heart rate.
d. Use the regression equation to predict the peak heart rate reached by a 28-year-old person during intensive exercise.
e. Which is the independent variable? Which is the dependent variable?
f. Is age a strong predictor of peak heart during exercise? If yes, explain why.
g. What is the coefficient of determination?