load(url("http://www.rossmanchance.com/iscam3/ISCAM.RData"))
library(dplyr)
library(ggplot2)homework at: http://www.rossmanchance.com/iscam3/instructors.htmlConserving Hotel Towels?
Many hotels have begun a conservation program that encourages guests to re-use towels rather than have them washed on a daily basis. A recent study examined whether one method of encouragement might work better than another. Different signs explaining the conservation program were placed in the bathrooms of the hotel rooms, with random assignment determining which rooms received which sign. One sign mentioned the importance of environmental protection, whereas another sign claimed that 75% of the hotel’s guests choose to participate in the program. The researchers suspected that the latter sign, by appealing to a social norm, would produce a higher proportion of hotel guests who agree to re-use their towels. Researchers used the hotel staff (a mid-sized, mid-priced hotel in the Southwest that was part of a well-known national hotel chain) to record whether guests staying for multiple nights agreed to reuse their towel after the first night.
Identify the observational units, explanatory variable, and response variable in this study.
State the null and alternative hypotheses in symbols, and be sure to define the parameter in the context of this study. The following table displays the observed data in this study:
| towel | Social norm | Environmental protection | Total |
|---|---|---|---|
| Guest opted to re-use towel | 98 | 74 | 172 |
| Guest did not opt to re-use towel | 124 | 137 | 261 |
| Total | 222 | 211 | 433 |
Calculate the conditional proportions of re-use in each group. Also calculate the difference between them and the ratio of these proportions.
Interpret what this ratio reveals in this context.
Use a two-sample z-test to test the hypotheses that you stated in (a). Report the test statistic and p-value.
Report your test decision at the \(\alpha\) = 0.10, 0.05, and 0.01 significance levels. Also summarize what these test decisions reveal about the strength of evidence for the researchers’ conjecture.
Produce and interpret a 90% confidence interval for the difference in probabilities of re-using towels between these two signs.
Produce and interpret a 90% confidence interval for the ratio of probabilities of re-using towels (relative risk) between these two signs.
Effectiveness of AZT (cont.)
Recall the study in Exercise 7 about the effectiveness of AZT.
Calculate and interpret the relative risk of HIV comparing the placebo group to the AZT group.
Suggest why the researchers might prefer to look at the relative risk in this study rather than the difference in conditional proportions.
Calculate and interpret a 95% confidence interval for the relative risk of HIV transmission between the population of placebo takers and the population of AZT takers. (Make sure you show your work.)
Briefly explain, in your own words, why we are working with the log of the relative risk in these calculations.
State the null and alternative hypotheses (in symbols and in words) for testing whether the risk of HIV-transmission is higher among placebo users than AZT users).
Based on your confidence interval, do these data provide convincing evidence that placebo takers are more likely to transmit HIV to their babies than AZT takers? Explain how you are deciding.
What population are you willing to generalize these results to?
Does the design of this study allow you to conclude that use of AZT causes a lower risk of HIV-transmission? Justify your answer.