Chapter 10.6, Problem 72E

In 2006, Boston Scientific sought approval for a new heart stent (a medical device used to open clogged arteries) called the Liberte. This stent was being proposed as an alternative to a stent called the Express that was already on the market. The following excerpt is from an article that appeared in The Wall Street Journal (August 14, 2008):

Boston Scientific wasn’t required to prove that the Liberte was ‘superior’ than a previous treatment, the agency decided—only that it wasn’t ‘inferior’ to Express. Boston Scientific proposed—and the FDA okayed—a benchmark in which Liberte could be up to three percentage points worse than Express—meaning that if 6% of Express patients’ arteries reclog, Boston Scientific would have to prove that Liberte’s rate of reclogging was less than 9%. Anything more would be considered 'inferior.’… In the end, after nine months, tire Atlas study found that 85 of the patients suffered reclogging. In comparison, historical data on 991 patients implanted with the Express stent show a 7% rate. Boston Scientific then had to answer this question: Could the study have gotten such results if the Liberte were truly inferior to Express?”

Assume a 7% reelogging rate for the Express stent. Explain why it would be appropriate for Boston Scientific to carry out a hypothesis test using the following hypotheses:

H₀: p = 0.10

H_a: p < 0.10

where p is the proportion of patients receiving Liberte stents that suffer reclogging. Be sure to address both the choice of the hypothesized value and the form of the alternative hypothesis in your explanation.