Explain in simple language how the dotplot shows that the sample mean you are using is an
unbiased estimator of the population mean.
b. Given your bag, with its average mass per grapefruit of 446.2 grams, do you think that the farmers’
market is correct in its claim? Justify your answer using the dotplot above.
Cortisol is a hormone produced by the body to control inflammation. People with chronic
inflammation and, hence, chronically elevated cortisol levels can develop problems with their
immune system. To explore this, 100 adult volunteers with chronic inflammation will participate in a
study to compare the effect of black tea versus coffee on cortisol levels. Each volunteer will be
assigned at random to one of the two groups and provided with daily capsules that contain a
concentrated form of either black tea or coffee. Each will also have his or her cortisol levels
measured at the beginning of the study and then 20 weeks later.
a. Describe how you would assign the 100 volunteers to the two groups in such a way as to allow a
statistically valid comparison of the two treatments.
b. Explain a statistical advantage to using capsules rather than having participants actually drink
coffee or tea.
c. Is it reasonable to generalize the findings of this study to all adults with chronic inflammation?
Explain.
- A large school district is planning an enrichment program for next summer. It is planning four course
options for students: Music, Sports, Drama, or Academic Enrichment. For planning purposes, the
district selected a random sample of 100 freshmen, a random sample of 100 sophomores, and a
random sample of 100 juniors. (Since seniors will have graduated, they were not surveyed.) The
selected students were asked which program they would choose to attend. The results for each class
are shown in the graph below:
a. Describe any associations you see between year in school and choice of program.
b. District administrators want to determine if there is convincing evidence that students in different
years have different preferences for programs throughout the whole district. Identify the hypothesis
test they should use and state the degrees of freedom.