Question

A sample of 16 healthy women aged 18-40 were randomly assigned to drink 24 ounces of either diet cola or water (8 to each group). Their urine was collected for three hours after ingestion of the beverage and calcium excretion (in mg) was measured. Researchers want to investigate whether diet cola leaches calcium out of the system, which would increase the amount of calcium in the urine for diet cola drinkers compared to water drinkers.

a.) Define the parameter of interest in words and context. Also give the appropriate notation for this parameter.

b.) Based on what is known about this study, do you think parametric or nonparametric methods would be best for these data?

c.) Regardless of you previous answer, let's take a look at the nonparametric approach. Explain how a bootstrap resample can be obtained in context.

d.) Where do you expect the bootstrap distribution to be centered?

e.) The 90% confidence interval for this study is (3.7438, 10.1250). Interpret this interval in context/

f.) Is there evidence to suggest that drinking diet cola leeches calcium out of the system? Explain.

Answer 1

Partial answer -

1. Since we want to check whether amount of calcium differ or not, let define be the amount of calcium among the group who consumed cola and be the amount of calcium among the group who consumed water.
2. Here we want to test . Since we don't have any idea about the distributions of parameters so, we will perform nonparametric test.
3. Here we can perform median test. Hence will be the median among their groups.