Four different glazes are applied to clay pots at two different thicknesses. The kiln

a. There are two possible experimental designs. Design A would use a random sample

of 100 consumers. From this group, 20 would be randomly assigned to each of the five recipes, so that each consumer tastes only one recipe. Design B would use a random sample of 100 consumers, with each consumer tasting all five recipes, the recipes being presented in a random order for each consumer. Which design would you recommend? Justify your answer.

b. When asked how the experiment is going, the researcher replies that one recipe smelled

so bad that she eliminated it from the analysis. Is this a problem for the analysis if design B was used? Why or why not? Is it a problem if design A was used? Why or why not? Supplementary Exercises H.R. 2.19 A large health care corporation is interested in the number of employees who devote a substantial amount of time providing care for elderly relatives. The corporation wants to develop a policy with respect to the number of sick days an employee could use to provide care to elderly relatives. The corporation has thousands of employees, so it decides to have a sample of employees fill out a questionnaire. a. How would you define employee? Should only full-time workers be considered? b. How would you select the sample of employees? c. What information should be collected from the workers? Bus. 2.20 The school of nursing at a university is developing a long-term plan to determine the num- ber of faculty members that may be needed in future years. Thus, it needs to determine the future demand for nurses in the areas in which many of the graduates find employment. The school decides to survey medical facilities and private doctors to assist in determining the future nursing demand.

a. How would you obtain a list of private doctors and medical facilities so that a sample

of doctors could be selected to fill out a questionnaire? b. What are some of the questions that should be included on the questionnaire? c. How would you determine the number of nurses who are licensed but not currently employed?

d. What are some possible sources for determining the population growth and health

risk factors for the areas in which many of the nurses find employment?

e. How could you sample the population of health care facilities and types of private

doctors so as to not exclude any medical specialties from the survey? 2.21 Consider the yields given in Table 2.7. In this situation, there is no interaction. Show that the one-at-a-time approach would result in the experimenter finding the best combination of nitrogen and phosphorus—that is, the combination producing maximum yield. Your solution should include the five combinations you would use in the experiment. 2.22 The population values that would result from running a 2 ⫻ 3 factorial treatment structure are given in the following table. Note that two values are missing. If there is no interaction between the two factors, determine the missing values. Factor 2 Factor 1 I II III A 25 45 B 30 50 Vet. 2.23 An experiment is designed to evaluate the effect of different levels of exercise on the health of dogs. The two levels are L 1 — daily 2-mile walk and L 2 — 1-mile walk every other day. At the end of a 3-month study period, each dog will undergo measurements of respiratory and cardiovascular fitness from which a fitness index will be computed. There are 16 dogs available for the study. They are all in good health and are of the same general size, which is within the normal range for their breed. The following table provides information about the sex and age of the 16 dogs. Dog Sex Age Dog Sex Age 1 F 5 9 F 8 2 F 3 10 F 9 3 M 4 11 F 6 4 M 7 12 M 8 5 M 2 13 F 2 6 M 3 14 F 1 7 F 5 15 M 6 8 M 9 16 M 3

a. How would you group the dogs prior to assigning the treatments to obtain a study

having as small an experimental error as possible? List the dogs in each of your groups.

b. Describe your procedure for assigning the treatments to the individual dogs using a

random number generator. Bus. 2.24 Four cake recipes are to be compared for moistness. The researcher will conduct the ex- periment by preparing and then baking the cake. Each preparation of a recipe makes only one cake. All recipes require the same cooking temperature and the same length of cooking time. The oven is large enough that four cakes may be baked during any one baking period, in positions P 1 through P 4 , as shown here. P 1 P 2 P 3 P 4

a. Discuss an appropriate experimental design and randomization procedure if there are

to be r cakes for each recipe.

b. Suppose the experimenter is concerned that significant differences could exist due to

the four baking positions in the oven front vs. back, left side vs. right side. Is your design still appropriate? If not, describe an appropriate design.

c. For the design or designs described in b, suggest modifications if there are five

recipes to be tested but only four cakes may be cooked at any one time. Env. 2.25 A forester wants to estimate the total number of trees on a tree farm that have diameters exceeding 12 inches. A map of the farm is available. Discuss the problem of choosing what to sample and how to select the sample. Engin. 2.26 A safety expert is interested in estimating the proportion of automobile tires with unsafe treads. Should he use individual cars or collections of cars, such as those in parking lots, in his sample? Ag. 2.27 A state department of agriculture wants to estimate the number of acres planted in corn within the state. How might one conduct such a survey? 2.28 Discuss the relative merits of using personal interviews, telephone interviews, and mailed questionnaires as data collection methods for each of the following situations:

a. A television executive wants to estimate the proportion of viewers in the country who

are watching the network at a certain hour.

b. A newspaper editor wants to survey the attitudes of the public toward the type of

news coverage offered by the paper.

c. A city commissioner is interested in determining how homeowners feel about a proposed

zoning change.

d. A county health department wants to estimate the proportion of dogs that have had

rabies shots within the last year. Soc. 2.29 A Yankelovich, Skelly, and White poll taken in the fall of 1984 showed that one-fifth of the 2,207 people surveyed admitted to having cheated on their federal income taxes. Do you think that this fraction is close to the actual proportion who cheated? Why? Discuss the difficulties of obtaining accurate information on a question of this type.