A high school mathematics teacher is convinced that a new software program will

is effective because the students using the software had significantly higher scores on the SAT than did the students who did not use the software. 2.3 A news report states that minority children who take advanced mathematics courses in high school have a first-year GPA in college that is equivalent to white students. The newspaper columnist suggested that the lack of advanced mathematics courses in high school curriculums in inner city schools was a major cause of inner city schools having a low success rate in college. What confounding variables may be present that invalidate the columnist’s conclusion? 2.4 A study was conducted to determine if the inclusion of a foreign language requirement in high schools may have a positive effect on a students’ performance on standardized English exams. From a sample of 100 high schools, 50 of which had a foreign language requirement and 50 that did not, it was found that the average score on the English proficiency exam was 25 higher for the students having a foreign language requirement. What confounding variables may be present that would invalidate the conclusion that requiring a foreign language in high school increases English language proficiency? 2.3 Sampling Designs for Surveys Soc. 2.5 An experimenter wants to estimate the average water consumption per family in a city. Discuss the relative merits of choosing individual families, dwelling units single-family houses, apartment buildings, etc., and city blocks as sampling units. H.R. 2.6 An industry consists of many small plants located throughout the United States. An execu- tive wants to survey the opinions of employees on the industry vacation policy. What would you suggest she sample? Pol. Sci. 2.7 A political scientist wants to estimate the proportion of adult residents of a state who favor a unicameral legislature. What could be sampled? Also, discuss the relative merits of personal interviews, telephone interviews, and mailed questionnaires as methods of data collection. Bus. 2.8 Two surveys were conducted to measure the effectiveness of an advertising campaign for a low-fat brand of peanut butter. In one of the surveys, the interviewers visited the home and asked whether the low-fat brand was purchased. In the other survey, the interviewers asked the person to show them the peanut butter container when the interviewee stated he or she had purchased low-fat peanut butter.

a. Do you think the two types of surveys will yield similar results on the percentage of

households using the product? b. What types of biases may be introduced into each of the surveys? Edu. 2.9 Time magazine, in an article in the late 1950s, stated that “the average Yaleman, class of 1924, makes 25,111 a year,” which, in today’s dollars, would be over 150,000. Time’s estimate was based on replies to a sample survey questionnaire mailed to those members of the Yale class of 1924 whose addresses were on file with the Yale administration in the late 1950s. a. What is the survey’s population of interest? b. Were the techniques used in selecting the sample likely to produce a sample that was representative of the population of interest? c. What are the possible sources of bias in the procedures used to obtain the sample? d. Based on the sources of bias, do you believe that Time’s estimate of the salary of a 1924 Yale graduate in the late 1950s is too high, too low, or nearly the correct value? 2.10 The New York City school district is planning a survey of 1,000 of its 250,000 parents or guardians who have students currently enrolled. They want to assess the parents’ opinion about mandatory drug testing of all students participating in any extracurricular activities, not just sports. An alphabetical listing of all parents or guardians is available for selecting the sample. In each of the following descriptions of the method of selecting the 1,000 participants in the survey, identify the type of sampling method used simple random sampling, stratified sampling, or clus- ter sampling.

a. Each name is randomly assigned a number. The names with numbers 1 through 1,000

are selected for the survey.

b. The schools are divided into five groups according to grade level taught at the school:

K–2, 3 –5, 6 –7, 8 –9, 10 –12. Five separate sampling frames are constructed, one for each group. A simple random sample of 200 parents or guardians is selected from each group.

c. The school district is also concerned that the parent or guardian’s opinion may differ

depending on the age and sex of the student. Each name is randomly assigned a num- ber. The names with numbers 1 through 1,000 are selected for the survey. The parent is asked to fill out a separate survey for each of their currently enrolled children. 2.11 A professional society, with a membership of 45,000, is designing a study to evaluate their membership’s satisfaction with the type of sessions presented at the society’s annual meeting. In each of the following descriptions of the method of selecting participants in the survey, iden- tify the type of sampling method used simple random sampling, stratified sampling, or cluster sampling.

a. The society has an alphabetical listing of all its members. They assign a number to

each name and then using a computer software program they generate 1,250 numbers between 1 and 45,000. They select these 1,250 members for the survey.

b. The society is interested in regional differences in its membership’s opinion. Therefore,

they divide the United States into nine regions with approximately 5,000 members per region. They then randomly select 450 members from each region for inclusion in the survey.

c. The society is composed of doctors, nurses, and therapists, all working in hospitals.

There are a total of 450 distinct hospitals. The society decides to conduct onsite in-person interviews, so they randomly select 20 hospitals and interview all members working at the selected hospital. 2.12 For each of the following situations, decide what sampling method you would use. Provide an explanation of why you selected a particular method of sampling.

a. A large automotive company wants to upgrade the software on its notebook computers.

A survey of 1,500 employees will request information concerning frequently used soft- ware applications such as spreadsheets, word processing, e-mail, Internet access, statisti- cal data processing, and so on. A list of employees with their job categories is available.

b. A hospital is interested in what types of patients make use of their emergency room

facilities. It is decided to sample 10 of all patients arriving at the emergency room for the next month and record their demographic information along with type of service required, the amount of time patient waits prior to examination, and the amount of time needed for the doctor to assess the patient’s problem. 2.13 For each of the following situations, decide what sampling method you would use. Provide an explanation of why you selected a particular method of sampling.

a. The major state university in the state is attempting to lobby the state legislator for a bill

that would allow the university to charge a higher tuition rate than the other universities in the state. To provide a justification, the university plans to conduct a mail survey of its alumni to collect information concerning their current employment status. The university grants a wide variety of different degrees and wants to make sure that information is obtained about graduates from each of the degree types. A 5 sample of alumni is considered sufficient.

b. The Environmental Protection Agency EPA is required to inspect landfills in the

United States for the presence of certain types of toxic material. The materials were sealed in containers and placed in the landfills. The exact location of the containers is no longer known. The EPA wants to inspect a sample of 100 containers from the 4,000 containers know to be in the landfills to determine if leakage from the contain- ers has occurred. 2.5 Designs for Experimental Studies Engin. 2.14 Researchers ran a quality control study to evaluate the quality of plastic irrigation pipes. The study design involved a total of 24 pipes, with 12 pipes randomly selected from each of two manufacturing plants. The pipes were manufactured using one of two water temperatures and one