A report in USA TODAY described an experiment to explore the accuracy of wearable devices designed to measure heart rate (“Wearable Health Monitors Not Always Reliable, Study Shows,” USA TODAY, October 12, 2016).

The researchers found that when 50 volunteers wore an Apple Watch to track heart rate as they walked, jogged, and ran quickly on a treadmill for 3 minutes, the results were accurate compared with an EKG 91% of the time. When 50 volunteers wore a Fitbit Charge, the heart rate results were accurate 84% of the time.

a. Explain why the data from this study should not be analyzed using a large-sample hypothesis test for a difference in two population proportions.

b. Carry out a hypothesis test to determine if there is convincing evidence that the proportion of accurate results for people wearing an Apple Watch is greater than this proportion for those wearing a Fitbit Charge. Use the Shiny app “Randomization Test for Two Proportions” (in the collection at statistics.cengage .com/PSO6e/Apps.html) to report an approximate P-value and use it to reach a decision in the hypothesis test. Remember to interpret the results of the test in context.

c. Use the Shiny app “Bootstrap Confidence Interval for Difference in Two Proportions”(in the collection at statistics.cengage.com  /PSO6e/Apps.html) to obtain a 95% bootstrap confidence interval for the difference in the population proportions of accurate results for people wearing an Apple Watch and those wearing a Fitbit Charge. Interpret the interval in the context of the research.