The article ?Rapid Evolutionary Response to a Transmissible Cancer in Tasmanian Devils? (nature .com/articles/ncomms12684, retrieved December 20, 2016) describes the spread of devil facial tumor disease (DFTD), which is a fatal form of cancer that swept through the Tasmanian devil population near the beginning of the 21st century. Researchers studied the genetic reaction of the Tasmanian devils by comparing the rates of occurrence of specific genetic markers of interest before and after DFTD swept across the island.

One region of Tasmania is called West Pencil Pine. Analysis of 21 tissue specimens taken from a representative sample of Tasmanian devils living in West Pencil Pine in 2006, before DFTD swept through, revealed that 5% had a specific genetic marker. Also analyzed were 42 tissue specimens from a representative sample of devils living in the same region in 2013 and 2014, after DFTD. In this sample, 43% had the same genetic marker. A significant and substantial change in these rates would indicate a remarkably fast evolution in the genetic code of the Tasmanian devils to protect against DFTD.

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

b. Use the output at the top of the page from the Shiny app ?Randomization Test for Two Proportions? to carry out a hypothesis test to determine if there is convincing evidence that the proportion of Tasmanian devils with the genetic marker was greater after DFTD than before DFTD.

c. Use the output from the Shiny app ?Bootstrap Confidence Interval for Difference in Two Proportions? to identify a 95% confidence interval for the difference in the rates of occurrence of the specific genetic marker in the genes of Tasmanian devils, before and after DFTD. Interpret the confidence interval in context.

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Randomization Distribution 150 100 50 -0.1 Difference in Simulated Sample Proportions -0.4 0.1 0.2 0.3 0.4 Observed Difference in Sample Proportions Standard Error P-Value # of Simulated Samples #of Values in Tail -0.381 0.121 1000 0.002 Frequency Bootstrap Distribution 100 50 -0.06 -0.04 -0.02 0.02 0.04 0.06 0.08 0.1 0.12 Difference in Simulated Sample Proportions Observed Difference in Sample Standard Lower Upper Conf # of Bootstrap Proportions Error Bound Bound Level Samples 0.022 0.031 -0.037 0.080 95% 1000 Frequency