We are only beginning to learn about the longterm effects of space travel on human health. A study published in 2016 (Nature Scientific Reports 6,Article number: 29901, nature.com/articles? /srep29901, July 28, 2016, retrieved May 6, 2017) found that by 2014, seven of the U.S. astronauts who traveled to the moon during Apollo lunar missions of the 1960s and 1970s had died, and that three of these (3/7 5 43%) had died from cardiovascular disease (CVD). The overall U.S. death rate due to CVD for adults age 55 to 64 in 2013 was 27%. Do the data for lunar astronauts indicate that, as a group, they are at increased risk of death caused by CVD? Assume that it is reasonable to regard this sample as representative of the population of past, present, and future U.S. lunar astronauts.

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

b. Use the output at the top of the next page from the Shiny app ?Randomization Test for One Proportion? to complete an appropriate hypothesis test.

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Randomization Distribution 300 200 100 0.2 0.6 0.4 0.8 Sample Proportion Observed Sample Proportion Null Hypothesis Standard Error P-Value #of Simulated Samples #of Values in Tail 0.301 1000 301 0270 0.429 0.168 Frequency