A number of people afflicted with kidney stones have reported that they passed their stones naturally while riding the Big Thunder Mountain Railroad roller coaster at Walt Disney World's Magic Kingdom theme park. To investigate, Mitchell and Wartinger (2016) brought a silicone pyelocalyceal renal model containing urine and a medium-sized kidney stone on the roller coaster ride 20 times. When the model was placed in the front seats, the stone passed once in eight rides. When the model was placed in the rear seats, the stone passed seven times in 12 rides. These data suggest that riding that roller coaster is an effective way to pass kidney stones, but does it matter where you sit?

1. State the null and alternative hypotheses for a test of whether kidney stone passage rates differ between roller coaster front and back seats.
2. Make a table of the expected frequencies under the null hypothesis.
3. Examine the table from #6. What issue arises that would prevent you testing the null hypothesis using the 2 contingency test?
4. What test method should be used instead?
5. When we carried out the correct test, we obtained P=0.07, so we failed to reject H0. Which conclusion is more justified: "It does not matter where you sit" or "The study is inconclusive"? Why?
6. Draw a distribution that is approximately normal, with mean equal to 10 cm and variance equal to 360. On the same graph, draw the distribution of the means of samples taken from this distribution, if each sample was a random sample of 10 individuals.