SECTION 3.3 Exercises

For Exercises 3.42 to 3.44, see pages 144145; for 3.45, see page 146; for 3.46 and 3.47, see page 147; for 3.48 and 3.49, see page 150; for 3.50 and 3.51, see page 152; for 3.52, see page 153; for 3.53 and 3.54, see page 154; and for 3.55, see page 156.

Question 3.56

3.56 What is needed?

Explain what is deficient in each of the following proposed experiments, and explain how you would improve the experiment.

  1. Two forms of a lab exercise are to be compared. There are 10 rows in the classroom. Students who sit in the first five rows of the class are given the first form, and students who sit in the last five rows are given the second form.
  2. The effectiveness of a leadership program for high school students is evaluated by examining the change in scores on a standardized test of leadership skills.
  3. An innovative method for teaching introductory biology courses is examined by using the traditional method in the fall zoology course and the new method in the spring botany course.

Question 3.57

3.57 What is wrong?

Explain what is wrong with each of the following randomization procedures, and describe how you would do the randomization correctly.

  1. A list of 50 subjects is entered into a computer file and then sorted by last name. The subjects are assigned to five treatments by taking the first 10 subjects for Treatment 1, the next 10 subjects for Treatment 2, and so forth.

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  2. Eight subjects are to be assigned to two treatments, four to each. For each subject, a coin is tossed. If the coin comes up heads, the subject is assigned to the first treatment; if the coin comes up tails, the subject is assigned to the second treatment.
  3. An experiment will assign 80 rats to four different treatment conditions. The rats arrive from the supplier in batches of 20, and the treatment lasts two weeks. The first batch of 20 rats is randomly assigned to one of the four treatments, and data for these rats are collected. After a one-week break, another batch of 20 rats arrives and is assigned to one of the three remaining treatments. The process continues until the last batch of rats is given the treatment that has not been assigned to the three previous batches.

3.57

(a) Not all subjects have an equal chance to be in each group (alphabetical is not random). (b) More than 4 subjects (even all 8) could end up in the same group. (c) Batches of rats could be different, so randomization should be done so that each rat is treated separately or batches of rats are divided randomly among treatments equally.

Question 3.58

3.58 Evaluate a new method for training new employees.

A new method for training new employees is to be evaluated by randomly assigning new employees to either the current training program or the new method. A questionnaire will be used to evaluate the satisfaction of the new employees with the training. Explain how this experiment should be done in a double-blind fashion.

Question 3.59

3.59 Can you change attitudes of workers about teamwork?

You will conduct an experiment designed to change attitudes of workers about teamwork. Discuss some variables that you might use if you were to use a block design for this experiment.

3.59

Possibly blocking variables include anything related to their prior experience with teamwork (those who are already on a team versus those who are not, etc.).

Question 3.60

3.60 An experiment for a new product.

Compost tea is rich in microorganisms that help plants grow. It is made by soaking compost in water.25 Design a comparative experiment that will provide evidence about whether or not compost tea works for a particular type of plant that interests you. Be sure to provide all details regarding your experiment, including the response variable or variables that you will measure. Assuming that the experiment shows positive results, write a short description about how you would use the results in a marketing campaign for compost tea.

Question 3.61

3.61 Marketing your training materials.

Water quality of streams and lakes is an issue of concern to the public. Although trained professionals typically are used to take reliable measurements, many volunteer groups are gathering and distributing information based on data that they collect.26 You are part of a team to train volunteers to collect accurate water quality data. Design an experiment to evaluate the effectiveness of the training. Write a summary of your proposed design to present to your team. Be sure to include all the details that they will need to evaluate your proposal. How would you use the results of the experiment to market your training materials?

Question 3.62

3.62 Randomly assign the subjects.

You can use the Simple Random Sample applet to choose a treatment group at random once you have labeled the subjects. Example 3.22 (page 151) describes an experiment in which 20 students are chosen from a group of 40 for the treatment group in a study of the effect of cell phones on driving. Use the applet to choose the 20 students for the experimental group. Which students did you choose? The remaining 20 students make up the control group.

Question 3.63

3.63 Randomly assign the subjects.

The Simple Random Sample applet allows you to randomly assign experimental units to more than two groups without difficulty. Example 3.23 (page 152) describes a randomized comparative experiment in which 150 students are randomly assigned to six groups of 25.

  1. Use the applet to randomly choose 25 out of 150 students to form the first group. Which students are in this group?
  2. The “population hopper” now contains the 125 students that were not chosen, in scrambled order. Click “Sample” again to choose 25 of these remaining students to make up the second group. Which students were chosen?
  3. Click “Sample” three more times to choose the third, fourth, and fifth groups. Don’t take the time to write down these groups. Check that there are only 25 students remaining in the “population hopper.” These subjects get Treatment 6. Which students are they?

Question 3.64

3.64 Random digits.

Table B is a table of random digits. Which of the following statements are true of a table of random digits, and which are false? Explain your answers.

  1. Each pair of digits has chance 1/100 of being 50.
  2. There are exactly four 0s in each row of 40 digits.
  3. The digits 9999 can never appear as a group, because this pattern is not random.

Question 3.65

3.65 I’ll have a Mocha Light.

Here’s the opening of a press release: “Starbucks Corp. on Monday said it would roll out a line of blended coffee drinks intended to tap into the growing popularity of reduced-calorie and reduced-fat menu choices for Americans.” You wonder if Starbucks customers like the new “Mocha Frappuccino Light” as well as the regular version of this drink.

  1. Describe a matched pairs design to answer this question. Be sure to include proper blinding of your subjects.
  2. You have 30 regular Starbucks customers on hand. Use software or Table B at line 151 to do the randomization that your design requires.

3.65

(a) Each subject will taste and rate each drink without being told or shown which are the regular and light versions. Half of the subjects will be given the regular version first, then the light version; the other half will be given the samples in reverse order. (b) Using labels 01–30 and line 151, the subjects for the first treatment are 03, 29, 26, 01, 12, 11, 21, 30, 09, 23, 07, 27, 20, 06, 05.

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Question 3.66

3.66 Price cuts on athletic shoes.

Stores advertise price reductions to attract customers. What type of price cut is most attractive? Market researchers prepared ads for athletic shoes announcing different levels of discounts (20%, 40%, or 60%). The student subjects who read the ads were also given “inside information” about the fraction of shoes on sale (50% or 100%). Each subject then rated the attractiveness of the sale on a scale of 1 to 7.

  1. There are two factors. Make a sketch like Figure 3.4 (page 144) that displays the treatments formed by all combinations of levels of the factors.
  2. Outline a completely randomized design using 50 student subjects. Use software or Table B at line 121 to choose the subjects for the first treatment.

Question 3.67

3.67 Effects of price promotions.

A researcher is studying the effect of price promotions on consumers’ expectations. She makes up a history of the store price of a hypothetical brand of laundry detergent for the past year. Students in a marketing course view the price history on a computer. Some students see a steady price, while others see regular promotions that temporarily cut the price. Then the students are asked what price they would expect to pay for the detergent.

  1. Is this study an experiment? Explain your answer.
  2. What are the explanatory and response variables?

3.67

(a) Experiment, the subjects are assigned a treatment. (b) The explanatory variable is the price history shown (with and without promotions); the response is the price they would expect to pay.

Question 3.68

3.68 Aspirin and heart attacks.

“Nearly five decades of research now link aspirin to the prevention of stroke and heart attacks.” So says the Bayer Aspirin website, bayeraspirin.com. The most important evidence for this claim comes from the Physicians’ Health Study, a large medical experiment involving 22,000 male physicians. One group of about 11,000 physicians took an aspirin every second day, while the rest took a placebo. After several years, the study found that subjects in the aspirin group had significantly fewer heart attacks than subjects in the placebo group.

  1. Identify the experimental subjects, the factor and its levels, and the response variable in the Physicians’ Health Study.
  2. Use a diagram to outline a completely randomized design for the Physicians’ Health Study.
  3. What does it mean to say that the aspirin group had “significantly fewer heart attacks”?

Question 3.69

3.69 Marketing to children.

If children are given more choices within a class of products, will they tend to prefer that product to a competing product that offers fewer choices? Marketers want to know. An experiment prepared three sets of beverages. Set 1 contained two milk drinks and two fruit drinks. Set 2 had two fruit drinks and four milk drinks. Set 3 contained four fruit drinks but only two milk drinks. The researchers divided 120 children aged 4 to 12 years into three groups at random. They offered each group one of the sets. As each child chose a beverage to drink from the set presented, the researchers noted whether the choice was a milk drink or a fruit drink.

  1. What are the experimental subjects?
  2. What is the factor and what are its levels? What is the response variable?
  3. Use a diagram to outline a completely randomized design for the study.
  4. Explain how you would assign labels to the subjects. Use software to do the randomization or Table B at line 145 to choose the first five subjects assigned to the first treatment.

3.69

(a) The 120 children are the subjects. (b) The factor is the sets of beverages. The levels are the three sets. The response variable is the child’s choice (milk or fruit drink). (d) Using line 145: The subjects chosen are 060, 102, 050, 005, and 006.

Question 3.70

3.70 Effects of TV advertising.

You decide to use a completely randomized design in the two-factor experiment on response to advertising described in Example 3.16 (page 143). The 30 students named below will serve as subjects. Outline the design. Then use software or Table B at line 110 to randomly assign the subjects to the six treatments.

tvads

Alomar Denman Han Liang Padilla Valasco
Asihiro Durr Howard Maldonado Plochman Vaughn
Bennett Edwards Hruska Marsden Rosen Wei
Chao Fleming James O’Brian Trujillo Willis
Clemente George Kaplan Ogle Tullock Zhang

Question 3.71

3.71 Temperature and work performance.

An expert on worker performance is interested in the effect of room temperature on the performance of tasks requiring manual dexterity. She chooses temperatures of 20°C (68°F) and 30°C (86°F) as treatments. The response variable is the number of correct insertions, during a 30-minute period, in a peg-and-hole apparatus that requires the use of both hands simultaneously. Each subject is trained on the apparatus and is then asked to make as many insertions as possible in 30 minutes of continuous effort.

  1. Outline a completely randomized design to compare dexterity at 20°C and 30°C. Twenty subjects are available.
  2. Because people differ greatly in dexterity, the wide variation in individual scores may hide the systematic effect of temperature unless there are many subjects in each group. Describe in detail the design of a matched pairs experiment in which each subject serves as his or her own control.

3.71

(b) Each worker performs the task twice, once at each temperature, for 30 minutes, and the number of insertions is recorded. The order of temperature assigned is randomized so that half of the workers first perform it at 20°C then 30°C, and the other half are reversed. The difference in number of insertions between the two temperatures is the response.