Set Up

Exercise

Refer to the piglets and hurricane datasets on Canvas for this assignment.

1. The climatologist you were consulting with last week has moved on to look at the effects of hurricanes. The hurricanes dataset includes the estimated damage caused by each hur- ricane in millions of 2013 dollars (damage_norm). The climatologist would like to know whether the average damage is over $1 billion (i.e., a value of 1000 for damage_norm). The climatologist decides to use a 𝛼 = .05 significance level with a two-sided test.
   1. Examine a histogram of the damage amounts and comment on its characteristics.
   2. Why might it be helpful to use the median damage, rather than the mean damage caused by the hurricanes? From the perspective of statistical inference, what might be the drawback of using the median, instead of the mean?
   3. What is the best guess for the median damage caused by hurricanes?
   4. What test statistic will you use for a test of the median? (Explain how you found your answer.)
   5. Find the p-value for the test of the median. Explain what this p-value represents in the context of this research scenario.
   6. What conclusion should the climatologist draw about hurricane damage?
   7. The climatologist doesn’t understand why his best guess for the damage of hur- ricanes seems to conflict with the conclusion you said he should draw from the statistical test. How would you explain this apparent conflict to him?

2. A hog farmer is trying to improve the consistency of the newborn weight of the piglets on his farm. Last year, the standard deviation of the newborn piglet weight was 0.44 kg. This year, the farmer has attempted to selectively breed sows that produced particularly uniform litters of piglets. The piglets dataset on Canvas includes the weights in kilograms of 85 randomly selected piglets born on the farm this year.
   1. What are the population, sample, parameter, and statistic for this study?
   2. Use the boot.ci() function to calculate a 99 percent confidence interval for the population standard deviation of newborn piglet weights this year.
   3. Does the confidence interval suggest that the farmer has improved the con- sistency of newborn piglet weights compared with last year? Explain how you know.
   4. What is the significance level of the implicit statistical test that you conducted in part (c)?
   5. Find the p-value for this statistical test using the boot.p() function.
   6. If the farmer had used a significance level of 𝛼 = .05, would he have come to a different conclusion? Explain.
   7. Why did we use the bootstrap procedure for this research scenario?

3. The mean cholesterol level in the U.S. population is approximately 180, with a standard deviation of 41. A pharmaceutical company thinks that the new drug they have developed will reduce cholesterol levels by 10 percent. They are planning to run a study of the drug, but they are looking to redesign their study, after determining that their initial plans would yield very low statistical power. They will conduct a two-sided test with a signifi- cance level of 𝛼 = .01.