EXTRA PRACTICE WITH ANSWERS CHAPTER 4 EXTRA PRACTICE WITH ANSWERS

1. As a researcher for a pharmaceutical company, you are designing a study to test the effectiveness of a new treatment for migraine headaches. You have been given a list of 126 people willing to participate in the trial. The first 70 people are female; the remaining 56 are male.   a) Preliminary research suggests that men and women respond differently to this new treatment. What sort of experimental design would you choose for this study, and why? A randomized block design—blocking by gender—will reduce the impact that differences between the responses of men and women to the treatment might have on variability arising from random assignment.

b) Assume that 56 men and 70 women suffering from migraines are available for the study. Make a diagram to show how you assign individuals to the treatment groups. Random assignment New migraine treatment n = 28 Standard treatment n = 35 Compare relief from migraine pain Men n = 56 Women n = 70 126 volunteers

c) Describe a design for this experiment c) Describe a design for this experiment. Be sure to include a description of how you assign individuals to the treatment groups.   First create two blocks comprised of the 70 women and the 56 men. Then, within each block assign the women numbers from 01 to 70 and the men numbers from 01 to 56. Choose 2-digit numbers from the random number table, ignoring repeats and unassigned numbers, until you have selected 35 women. Then begin elsewhere in the table and follow the same procedure to randomly select 28 men. These subjects will be given the new migraine treatment, and the remaining subjects will receive a commonly-used standard treatment. Compare relief from migraine pain between the treatment group and the control group. OR

First create two blocks comprised of the 70 women and the 56 men First create two blocks comprised of the 70 women and the 56 men. Write the women’s names on 70 identical slips of paper, place the slips in a hat, and mix them well. Pull out 35 slips to determine which women will be given the new migraine treatment and the remaining 35 subjects will receive a commonly-used standard treatment. Randomly assign the 56 men into two groups of 28 using a similar process. Compare relief from migraine pain between the treatment group and the control group.

For numbers 2 & 3, determine whether the scenario describes an observational study or an experiment. 2. A researcher gives a group of eight individuals a flu shot and gives a placebo to another group of eight individuals to find out if they get the flu this winter. Experiment 3. A government agency wants to conduct a study on the effects of drinking and driving. Observational study

4. A maker of fabric for clothing is setting up a new line to “finish” the raw fabric. The line will use either metal rollers or natural-bristle rollers to raise the surface of the fabric; a dyeing-cycle time of either 25 or 45 minutes; and a temperature of either 172° or 198°C. An experiment will compare all combinations of these choices. Three specimens of fabric will be subjected to each treatment and scored for quality. List the experimental units, factors, and treatments in this experimental design. Experimental units: the 24 pieces of fabric. Factors: roller type, dyeing-cycle time, and temperature. Treatments: (1) metal, 25min, 172°; (2) natural, 25 min, 172°; (3) metal, 45 min, 172°; (4) natural, 45 min, 172°; (5) metal, 25 min, 198°; (6) natural, 25 min, 198°; (7) metal, 45 min, 198°;(8) natural, 45 min, 198°.

5. A high school’s student newspaper plans to survey local businesses about the importance of students as customers. From an alphabetical list of all local businesses, the newspaper staff chooses 221 businesses at random. Of these, 107 return the questionnaire mailed by the staff. a) What is the sample? The 107 businesses that returned the questionnaires. b) What is the population for this sample survey? All local businesses.

For numbers 6 – 10, determine what type of sample was taken. 6 For numbers 6 – 10, determine what type of sample was taken. 6. How much sleep do high school students get on a typical school night? An interested student designed a survey to find out. To make data collection easier, the student surveyed the first 100 students to arrive at school on a particular morning. These students reported an average of 7.2 hours of sleep on the previous night. Convenience Sample. 7. How much sleep do high school students get on a typical school night? An interested student designed a survey to find out. To make data collection easier, the student made an announcement over the PA system asking students who were interested in answering his question to meet him in the main office. These 47 students reported an average of 7.2 hours of sleep on the previous night. Voluntary Response Sample.

8. The student asks a teacher to write every single students name in the school on identical slips of paper, put them in a hat, and pick out 12 students to ask the question: “How many hours of sleep did you get last night?” SRS. 9. A lumber company wants to estimate the proportion of trees in a large forest that are ready to be cut down. They use an aerial map to divide the forest into 200 equal-sized rectangles. Then they choose a random sample of 20 rectangles and examine every tree that’s in one of those rectangles. Cluster Sample.

10. A TV station wishes to obtain information on the TV viewing habits in its market area. The market area contains one city of population 170,000, another city of 70,000, and four towns of about 5000 inhabitants each. The station suspects that the viewing habits may be different in larger and smaller cities and in the rural areas. Stratified Random Sample.

For numbers 11 – 13, determine what type of experiment was conducted For numbers 11 – 13, determine what type of experiment was conducted. 11. Does talking on a hands-free cell phone distract drivers? Researchers recruit 40 student subjects for an experiment to investigate this question. They have a driving simulator equipped with a hands-free phone for use in the study. Each subject will complete two sessions in the simulator: one while talking on the hands-free phone and the other while just driving. The order of the two sessions for each subject will be determined at random. The route, driving conditions, and traffic flow will be the same in both sessions. Matched Pairs.

12. Four hundred subjects are separated based on age 12. Four hundred subjects are separated based on age. Within each age group, subjects are randomly assigned to the two treatment groups (flu shot and placebo). Four months later, doctors compare the number of subjects that had the flu. Randomized Block Design. 13. Suppose we have 4 different diets which we want to compare. The diets are labeled Diet A, Diet B, Diet C, and Diet D. We are interested in how the diets affect the coagulation rates of rabbits. The coagulation rate is the time in seconds that it takes for a cut to stop bleeding. We have 16 rabbits available for the experiment, so we will use 4 on each diet. Completely Randomized Design.