Question
Studies have shown that foods rich in compounds known as flavonoids help lower blood pressure. Researchers conducted a study to investigate whether there was a greater reduction in blood pressure for people who consumed dark chocolate, which contains flavonoids, than people who consumed white chocolate, which does not contain flavonoids. Twenty-five healthy adults agreed to participate in the study and add 3.5 ounces of chocolate to their daily diets. Of the 25 participants, 13 were randomly assigned to the dark chocolate group and the rest were assigned to the white chocolate group. All participants had their blood pressure recorded, in millimeters of mercury ( \(\mathrm{mmHg}\) ), before adding chocolate to their daily diets and again 30 days after adding chocolate to their daily diets.
The reduction in blood pressure (before minus after) for each of the participants in the two groups is shown in the dotplots below.
(a) Determine and compare the medians of the reduction in blood pressure for the two groups.
The researchers found the mean reduction in blood pressure for those who consumed dark chocolate is \(\bar{x}_{\text {dark }}=6.08 \mathrm{mmHg}\) and the mean reduction in blood pressure for those who consumed white chocolate is \(\bar{x}_{\text {white }}=0.42 \mathrm{mmHg}\).
(b) One researcher indicated that because the difference in sample means of \(5.66 \mathrm{mmHg}\) is greater than 0 there is convincing statistical evidence to conclude that the population mean blood pressure reduction for those who consume dark chocolate is greater than for those who consume white chocolate. Why might the researcher’s conclusion, based only on the difference in sample means of \(5.66 \mathrm{mmHg}\), not necessarily be true?
A simulation was conducted to investigate whether there is a greater reduction of blood pressure for those who consume dark chocolate than for those who consume white chocolate. The simulation was conducted under the assumption that no difference exists. The results of 120 trials of the simulation are shown in the following dotplot.
(c) Use the results of the simulation to determine whether the results from the 25 participants in the study provide convincing statistical evidence, at a 5 percent level of significance, that adding dark chocolate to a daily diet will result in a greater reduction in blood pressure, on average, than adding white chocolate to a daily diet. Justify your answer.
▶️Answer/Explanation
Ans:
(a) The median blood pressure reduckim is 1 for the doric Chocolate grove and 0 for the white Chocolate sue. The dart chocolate gran wis \(\partial\) higher median blood pressure reduction.
(b) you cannot conclude statistic significance based on sample means don. An appreciate hypothesis test must be conducted to decide whether or not “. lively the difference in Sample mean l was caused by random chance.
(b) You can not conclude statistics significance based on sample means alone. An appreciate hypothesis test must be conducted to decide whether or not o lively the difference in Sample mean l was caused by random chance.
Question
Researchers will conduct a year-long investigation of walking and cholesterol levels in adults. They will select a random sample of 100 adults from the target population to participate as subjects in the study.
(a) One aspect of the study is to record the number of miles each subject walks per day. The researchers are deciding whether to have subjects wear an activity tracker to record the data or to have subjects keep a daily journal of the miles they walk each day. Describe what bias could be introduced by keeping the daily journal instead of wearing the activity tracker.
During the course of the study, the subjects will have their cholesterol levels measured each month by a doctor. The researchers will perform a significance test at the end of the study to determine whether the average cholesterol level for subjects who walk fewer miles each day is greater than for those who walk more miles each day.
(b) Selecting a random sample creates a reasonable representative sample of the target population. Explain the benefit of using a representative sample from the population.
(c) Suppose the researchers conduct the test and find a statistically significant result. Would it be valid to claim that increased walking causes a decrease in average cholesterol levels for adults in the target population? Explain your reasoning.
▶️Answer/Explanation
Ans:
(a) using a journal to track mileage is likely to underestimate true miles walked each day because the adults will likely not record the small distances they walked each day, like walking from the kitchen to the couch.
(b) using a representative sample makes it easier to collect data within the study, and that data can be used to make an accurate conclusion about the relationship between walking miles and cholesterol levels in the target population
(c) No. Because this was an observational study and not an experiment, we cannot determine causation between miles walked and cholesterol levels.