From the Introduction to Modern Statistics (IMS) textbook, complete
the following exercises:
- Ch 11.5 Exercises: #3, #4, #6, #8
Additionally, complete the following exercises:
Question #1: For this question you should use the
“Randomization Hypothesis Tests” menu of StatKey to perform
hypothesis tests involving the American Community Survey data set
introduced in Lab 11:
https://remiller1450.github.io/data/EmployedACS.csv
For each hypothesis test (Parts A-C) you should include the following
steps:
- State the null and alternative hypotheses using either words or
statistical notation
- Report the point estimate, then StatKey and your null hypothesis to
find the \(p\)-value.
- Interpret the \(p\)-value in
relation to your hypotheses. Be sure to comment on both
practical and statistical significance.
For some parts, you should expect to use R to obtain
some of the relevant information needed to find the \(p\)-value using StatKey.
- Part A: According
to Wikipedia, 78% of US adults speak English as their native
language. Use a hypothesis test to determine whether the ACS sample
provides evidence that refutes this claim.
- Part B: Perform a hypothesis test to evaluate
whether these data provide compelling statistical evidence that married
individuals are more likely to have health insurance than unmarried
individuals.
- Part C: According to “worddata.info” (which strikes
me as a questionable source) the average personal income in the United
States is $64,000. Use a hypothesis test to determine whether the ACS
sample provides sufficient evidence to refute this claim.
- Part D: In Parts A-C you performed 3 different
hypothesis tests. If you wanted to use the Bonferroni Adjustment to
ensure no more than a 5% Type 1 error rate for this family of tests,
what threshold should be used for judging statistical
significance?