Data from a large study carried out in 2008 were used to estimate that 10% of all smokers who quit smoking are smoking again after 1 year (“Relapse to Smoking After 1 Year of Abstinence: A Meta-analysis,” ncbi.nlm.nih.gov/pmc/articles /PMC2577779/, June 8, 2008, retrieved May 6, 2017). The outcomes of many surgical procedures are improved for patients who are not smoking.

In a University of Kansas Medical Center study (“Recidivism Rates After Smoking Cessation BeforeSpinal Fusion,” healio.com/orthopedics/journals  /ortho/2016-3-39 2/%7B28bf5c50-c2b8-413a-a662 -f10efce6c9ef%7D/recidivism-rates-after-smoking -cessation-before-spinal-fusion, March 31, 2016, retrieved May 6, 2017), patients needing spinal fusion surgery were required to quit smoking before their surgery was scheduled. After 1 year, n = 25 of the patients responded to a follow-up survey, and 17 were smoking again. Assume it is reasonable to regard this sample as representative of people who quit smoking before surgery. The data from this sample are used to decide if there is convincing evidence that the proportion of people who quit smoking prior to surgery who are smoking again after 1 year is greater than 0.10.

a. Explain why the data in this example should not be analyzed using a large-sample hypothesis test for one population proportion.

b. Use the output at the bottom of the page from the Shiny app “Randomization Test for One Proportion” to help to complete an appropriate hypothesis test.

c. Explain how the result of the hypothesis test performed may be related to the fact that the spinal fusion patients were required to stop smoking before their surgeries.