2. (25) Nine-banded armadillos are native to South America, but they have recently made their way north into the United States as well, and have started to inhabit parts of North Carolina in the last twenty years. Researchers have long known that lifespans for ninebanded armadillos living in South America are approximately normally distributed with a mean of 10.4 years and standard deviation 2.3 years, but you believe that they do not live as long here in NC given their propensity to run out into busy roads and get hit by cars. To test your belief, you tagged 25 armadillos at random when they rst started showing up in NC and have been tracking them ever since. Sadly, all 25 are now dead, and you have calculated an average lifespan of 9.6 years. Your sample standard deviation is very close to 2.3, so you decide to assume that NC armadillo lifespans have the same standard deviation as South American armadillo lifespans. 2.1. (5) You want to set up a hypothesis test to conrm your belief about armadillo life expectancies in North Carolina. What would be your null and alternative hypotheses for this test? 2.2. (5) What is the sampling distribution of the mean lifespan 5: for a random sample of 25 NC armadillos? Give me the type of distribution and any relevant parameter(s). 2.3. (5) Calculate the pvalue for this sample, rounding to 3 decimal places. Can you reject the null hypothesis in favor of your alternative hypothesis at a 5% level of signicance? 2.4. (5) Can you use the result in part (c) to deduce whether or not the null value no will fall outside of a 95% condence interval constructed around your sample mean? Explain. 2.5. (5) Your friend who likes armadillos and weird statistics (we all have one) wants you to construct a 92% condence interval around your sample mean. What are its upper and lower bounds? Round them to 3 decimal places