Worksheet 16: Sample Size Matters#
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Model the hot dog poll with either a bag of marbles or with coinflips.
Are we guaranteed that the sample mean \(\hat{\mu_n} = \mu\), the population mean? Why?
In the microplastics experiment, can we directly compute the probability that \(|\hat{\mu_n} - \mu|\) is big?
What do you expect to happen to our estimate \(\hat{\mu_n}\) as \(n\) gets larger?
As we increase \(n\), what do you notice about:
a. The variability of the dataset of our estimates \(\hat{\mu}_n\)?
b. The shape of the histogram?
Formulate the following as a “population vs. sample” scenario. a. What is the population? b. What is the variable \(x\) that describes members of the population? What is the population mean \(\mu\)? c. What are our samples \(x_1,\ldots,x_n\)?
A medical researcher has come up with a new drug. The drug has some side effects; a headache that lasts anywhere from \(0\) to \(48\) hours.
The researcher designs an experiment to determine the average duration of the side-effect headache; they recruit a group of \(n\) random sick patients, gives them all the drug, records the length of each of their headaches, and calculates the mean.