A horticulturalist is measuring the vitamin C concentration in oranges in an orchard

b. A medical specialist wants to compare two different treatments T

1 , T 2 for treating a particular illness. She will use eight hospitals for the study. She believes there may be differences in the response among hospitals. Each hospital has four wards of patients. She will randomly select four patients in each ward to participate in the study. Within each hospital, two wards are randomly assigned to get T 1 ; the other two wards will receive T 2 . All patients in a ward will get the same treatment. A single response variable is measured on each patient.

c. In the design described in b make the following change. Within each hospital, the

two treatments will be randomly assigned to the patients, with two patients in each ward receiving T 1 and two patients receiving T 2 .

d. An experiment is planned to compare three types of schools—public, private-

nonparochial, and parochial—all with respect to the reading abilities of students in sixth-grade classes. The researcher selects two large cities in each of five geographical regions of the United States for the study. In each city, she randomly selects one school of each of the three types and randomly selects a single sixth-grade class within each school. The scores on a standardized test are recorded for each of 20 students in each classroom. The researcher is concerned about differences in family income levels among the 30 schools, so she obtains the family income for each of the students who participated in the study. Bio. 2.16 A research specialist for a large seafood company plans to investigate bacterial growth on oysters and mussels subjected to three different storage temperatures. Nine cold-storage units are available. She plans to use three storage units for each of the three temperatures. One package of oysters and one package of mussels will be stored in each of the storage units for 2 weeks. At the end of the storage period, the packages will be removed and the bacterial count made for two samples from each package. The treatment factors of interest are temperature levels: 0, 5, 10°C and seafood levels: oysters, mussels. She will also record the bacterial count for each package prior to placing seafood in the cooler. Identify each of the following components of the experimental design.

a. factors b. factor levels

c. blocks d. experimental unit

e. measurement unit f. replications

g. treatments

2.17 In each of the following situations, identify whether the design is a completely randomized design, randomized block design, or Latin square. If there is a factorial structure of treatments, specify whether it has a two-factor or three-factor structure. If the experiment’s measurement unit is different from the experimental unit, identify both.

a. The 48 treatments comprised 3, 4, and 4 levels of fertilizers N, P, and K, respectively,

in all possible combinations. Five peanut farms were randomly selected and the 48 treat- ments assigned at random at each farm to 48 plots of peanut plants.

b. Ten different software packages were randomly assigned to 30 graduate students. The

time to complete a specified task was determined.

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

used in the glazing can hold eight pots at a time, and it takes 1 day to apply the glazes. The experimenter wants eight replications of the experiment. Because the conditions in the kiln vary somewhat from day to day, the experiment is conducted over an 8-day period. Each combination of a thickness and type of glaze is randomly assigned to one pot in the kiln each day. Bus. 2.18 A colleague has approached you for help with an experiment she is conducting. The ex- periment consists of asking a sample of consumers to taste five different recipes for meat loaf. When a consumer tastes a sample, he or she will give scores to several characteristics and these scores will be combined into a single overall score. Hence, there will be one value for each recipe for a consumer. The literature indicates that in this kind of study some consumers tend to give low scores to all samples; others tend to give high scores to all samples.

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.