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Use the following data to answer the next five exercises: A pair of studies was performed to measure the effectiveness of a new software program designed to help stroke patients regain their problem-solving skills. Patients were asked to use the software program twice a day, once in the morning and once in the evening. The studies observed $200$stroke patients recovering over a period of several weeks. The first study collected the data in Table 1.31. The second study collected the data in Table 1.32.

Patients who used the software were also a part of an exercise program whereas patients who did not use the software were not. Does this change the validity of the conclusions from Exercise 1.31?

Is a sample size of 1,000 a reliable measure for a population of 5,000?

Is a sample of 500 volunteers a reliable measure for a population of 2,500?

A question on a survey reads: "Do you prefer the delicious taste of Brand X or the taste of Brand Y?" Is this a fair question?

Is a sample size of two representative of a population of five?

What type of measure scale is being used? Nominal, ordinal, interval or ratio.

a. High school soccer players classified by their athletic ability: Superior, Average, Above average

b. Baking temperatures for various main dishes: 350, 400, 325, 250, 300

c. The colors of crayons in a 24-crayon box

d. Social security numbers

e. Incomes measured in dollars

f. A satisfaction survey of a social website by number: 1 = very satisfied, 2 = somewhat satisfied, 3 = not satisfied

g. Political outlook: extreme left, left-of-center, right-of-center, extreme right

h. Time of day on an analog watch

i. The distance in miles to the closest grocery store

j. The dates 1066, 1492, 1644, 1947, and 1944

k. The heights of 21–65 year-old women

l. Common letter grades: A, B, C, D, and F

Design an experiment. Identify the explanatory and response variables. Describe the population being studied and the experimental units. Explain the treatments that will be used and how they will be assigned to the experimental units. Describe how blinding and placebos may be used to counter the power of suggestion.

Discuss potential violations of the rule requiring informed consent.

a. Inmates in a correctional facility are offered good behavior credit in return for participation in a study.

b. A research study is designed to investigate a new children’s allergy medication.

c. Participants in a study are told that the new medication being tested is highly promising, but they are not told that only a small portion of participants will receive the new medication. Others will receive placebo treatments and traditional treatments.

A fitness center is interested in the mean amount of time a client exercises in the center each week.

Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally.