HOMEWORK 4 Due: next class 2/8

Transcription

1 HOMEWORK 4 Due: next class 2/8 1. Recall the class data we collected concerning body image (about right, overweight, underweight). Following the body image example in OLI, answer the following question by completing the parts below: Does it appear that body image tends to be influenced by gender? a. What is the explanatory variable? Gender b. What is the response variable? Body image c. Construct a two-way table summarizing the relationship between gender and body image. Use the explanatory variable for the rows and the response variable for the columns. 12pm About right Overweight Underweight Total Female Male pm About Right Overweight Underweight Total Female Male d. Determine the conditional row percents, and make a new two-way table that shows them. 12 pm About right Overweight Underweight Total Female 57.90% 42.10% 0% 100% Male 35.30% 58.80% 5.90% 100% 1 pm About Right Overweight Underweight Total Female 62.50% 25% 12.50% 100% Male 53.80% 30.80% 15.40% 100% 1

2 e. Draw a double bar chart that compares the conditional row percents. 12 pm Female Male 1 About right Overweight Underweight 1 pm Female Male 1 About Right Overweight Underweight f. Are men and women in our class just as likely to think their weight is about right? Among those students who do not think their weight is about right, is there a difference between the genders in their feelings about body image? 12pm : No, there is a big difference in the proportion of men and women in this class who think their weight is about right. About 22% more women think their weight is about right. There is a difference between the genders in their feeling about their body image for the overweight and underweight group too. More men think they are overweight. No females think they are underweight, and one male considers himself underweight. 1pm : There is not much of a difference between men and women in this class who think their weight is about right. The difference is only about 10% (63%--54%). About 10% more women think their body is about right. Similarly, there is not much difference between the genders for overweight and underweight. A little bit more men think they are over-, or underweight, but the differences are less than 5%. 2

3 2. For each of the situations described below, (i) describe the explanatory variable and indicate if it is quantitative or categorical, and (ii) describe the response variable and indicate if it is quantitative or categorical: a. A student was curious about which route would get her to school faster, so she collected data on how long the trip took for a freeway route and for a non-freeway route, taking each route ten times. Explanatory variable: route (freeway or non-freeway) C Response variable: time to get school Q b. A psychologist is studying the effect of electroshock therapy on a subject's ability to solve simple tasks. The number of tasks completed in a 10-minute period is recorded for subjects, half of whom received electroshock and half of whom did not receive electroshock. Explanatory variable: whether or not the subject received electroshock C Response variable: number of tasks completed in a 10-minute period Q c. You want to determine whether students' expected grades at the beginning of an introduction to statistics course are positively related to their final course grades. Explanatory variable: grade at the beginning of the course C (if you think about letter grades) or Q (if you think about scores) Response variable: grade at the end of the course C (if you think about letter grades) or Q (if you think about scores) d. A study is made to analyze how students SAT scores are related to whether they graduate from college. Explanatory variable: SAT scores Q Response variable: whether or not students graduate C 3. The government Office of Vital Statistics studies a sample of married couples, measuring the heights of each husband and each wife. Is there a clear choice of explanatory variable and response variable here? Explain. No. It would be just as natural to try to predict the husband s height from that of the wife as the other way around. 4. A clinical trial compares the effectiveness of two drugs, Lithium and Imipramine, in preventing a recurrence of depression among patients who were hospitalized with depression. Here are the results: 3

4 a. Construct a two-way table that classifies drug against the recurrence variable. Use the explanatory variable for the rows and the response variable for the columns. Recurrence No Recurrence Total Lithium Imipramine b. Determine the conditional row percents, and make a new two-way table that shows them. Recurrence No Recurrence Lithium 18/27 = 66.7% 9/27 = 33.3% Imipramine 8/29 = 27.6% 21/29 = 72.4% c. Draw a double bar chart that compares the conditional row percents. 4

5 Recurrence No Recurrence Lithium Imipramine d. Summarize what your analysis shows about the relationship between drug and the frequency of recurrence. Imipramine appears far more effective in preventing a recurrence of depression than Lithium, as two thirds of those treated with Lithium had a recurrence, while a little more than a quarter of those treated with Imipramine had one. e. Based on the number of subjects used in this study, are you reasonably convinced that one of the two drugs is better than the other at preventing a recurrence of depression? (Note: This question simply calls for a judgment call on your part, there is no correct answer at this point. We will need the methods of inference that will be covered later in this course in order to answer it. 5