3.24 Blueberries and bones. A study of the effects of blueberries on the bones of mice compared diets containing no blueberries, blueberries as 5% of the diet, and blueberries as 10% of the diet. Ten mice were randomly assigned to each diet. The mice were fed the diets for 30 days, and the total body bone mineral density (TBBMD) was measured at the end of the feeding period. What are the experimental units, the treatments, and the outcomes for this experiment? Would you use the term subjects for the experimental units? Explain your answers.

3.25 Online homework. Thirty students participated in a study designed to evaluate a new online homework system. None of the students had used an online homework system in the past. After using the system for a month, they were asked to rate their satisfaction with the system using a five-point scale.

3.26 Do magnets reduce pain? Some claim that magnets can be used to reduce pain. Design a double-blind experiment to test this claim. Write a proposal requesting funding for your study giving all the important details, including the number of subjects, issues concerning randomization, and how you will make the study double-blind.

3.27 Online sales of running shoes. A company that sells running shoes online wants to compare two new marketing strategies. They will test the strategies on 10 weekdays. In the morning of each day, a web page describing the comfort of the running shoes will be displayed. In the afternoon of each day, a web page describing the discounted price for the shoes will be displayed. Sales of the featured running shoes in the morning will be compared with sales in the afternoon at the end of the experiment.

3.28 Online sales of running shoes. Refer to the previous exercise. Suppose that for each day, you randomized the web pages, showing one in the morning and the other in the afternoon.

3.29 Online sales of running shoes. Refer to Exercise 3.27. Here is another way in which the experiment could be designed. Suppose that you alternate the display each time a customer visits the website. Can you view this experiment as a matched pairs design? Explain your answer.

3.30 Randomize the web pages for the running shoes. Refer to Exercise 3.28. Use software or Table B to randomize the treatments. Give a step-by-step detailed description of how you performed the randomization.

3.31 What is needed? Explain what is deficient in each of the following proposed experiments and explain how you would improve the experiment.

3.32 The Madden curse. Some people believe that individuals who appear on the cover of the football game Madden NFL will soon have a serious injury. Can you evaluate this belief with an experiment? Explain your answer.

3.33 Evaluate a new orientation program. Your company runs a two-day orientation program Monday and Tuesday each week for new employees. A new program is to be compared with the current one. Set up an experiment to compare the new program with the old. Be sure to provide details regarding randomization and what outcome variables you will measure.

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

3.35 Calcium and vitamin D. Vitamin D is needed for the body to use calcium. An experiment is designed to study the effects of calcium and vitamin D supplements on the bones of first-year college students. The outcome measure is the total body bone mineral content (TBBMC), a measure of bone health. Three doses of calcium will be used: 0, 250, and 500 milligrams per day (mg/day). The doses of vitamin D will be 0, 75, and 150 international units (IU) per day. The calcium and vitamin D will be given in a single tablet. All tablets, including those with no calcium and no vitamin D, will look identical. Subjects for the study will be 45 men and 45 women.

3.36 Use the Simple Random Sample applet. You can use the Simple Random Sample applet to choose a group at random once you have labeled the subjects. Example 3.12 (page 178) uses Excel to choose five students from a group of 10 to receive a treatment in an experiment. The remaining five students will receive a placebo control.

3.37 Use the Simple Random Sample applet. The Simple Random Sample applet allows you to randomly assign experimental units to more than two groups without difficulty. Consider a randomized comparative experiment in which 100 students are randomly assigned to four groups of 25.

3.38 Use the Simple Random Sample applet. The Simple Random Sample applet can demonstrate how randomization works to create similar groups for comparative experiments. Suppose that (unknown to the experimenters) the 20 even-numbered students among the 40 subjects for the smartphone study in Example 3.11 (page 176) tend to send more text messages than the odd-numbered students. We would like the two groups to be similar with respect to text messaging. Use the applet to choose 10 samples of size 20 from the 40 students. (Be sure to click “Reset” after each sample.) Record the counts of even-numbered students in each of your 10 samples. You see that there is considerable chance variation but no systematic bias in favor of one or the other group in assigning the fast-reacting students. Larger samples from larger populations will, on the average, do a better job of making the two groups equivalent.

3.39 Health benefits of bee pollen. “Bee pollen is effective for combating fatigue, depression, cancer, and colon disorders.” So says a website that offers the pollen for sale. We wonder if bee pollen really does prevent colon disorders. Here are two ways to study this question. Explain why the first design will produce more trustworthy data.

3.40 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.

3.41 Calcium and the bones of young girls. Calcium is important to the bone development of young girls. To study how the bodies of young girls process calcium, investigators used the setting of a summer camp. Calcium was given in punch at either a high or a low level. The camp diet was otherwise the same for all girls. Suppose that there are 30 campers.

3.42 Calcium and the bones of young girls. Refer to the previous exercise.

3.43 Measuring water quality in streams and lakes. 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.¹² 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.