Instructions:  On a separate sheet of paper, answer these questions. Show all your work in order to get as much credit as possible. 

Problem 1: Thirty years ago, a researcher went out and measured a bunch of elephants.  They found that the mean ear length of the elephants at that time was 43.9.   Last year, you got an NSF grant to go out and study elephant ear morphology.  You hypothesize that elephant ear length is different than it used to be.  To investigate this hypothesis of yours, you traveled to Africa, sampled 54 elephants, and measured the ear length of each.  You found that the mean ear length was 34.3 with a standard deviation of 6.7.  You decided that you wanted to use α=.05.  Conduct a hypothesis test to determine if mean ear length of elephants today is different than mean ear lengths of elephants 30 years ago.  Use a two-tailed test.   (Hint:  Write out the hypothesis, show your calculations, draw your distributions and label the critical values and the rejection region.  Make sure to explicitly state your conclusion in context of elephants).  

Problem 2: We are investigating wallabies.  We know that the overall population of adult wallabies can jump, on average, 22 feet in one leap.  We find a group of 14 wallabies that are particularly tall, living off by themselves in some corner of habitat.  We wish to know if these taller wallabies can jump farther than the rest of the population.  We measure all the leaps of wallabies in that subgroup, and find the mean jump length to be 24 feet with a standard deviation of 1.5. Conduct a hypothesis test to determine if these other wallabies can jump farther than all the rest.  Use alpha=.05.

Problem 3: We have a hatchery program with a large number of baby captive iguanas.  They all hatched at the same time (3 months prior), and have been living in the exact same physical conditions ever since.  Nobody has ever raised this particular species of iguana before, and we are trying to figure out if there is a difference in size as a result of two different hatchery diet regimes.   Getting diet regime A, we sample 74 baby iguanas.  We measure their size, and find that their mean size is 60.8 with a standard deviation of 5.5.  Getting diet regime B, we sample 59 baby iguanas.  We measure their size, and find that the mean size is 89.3 with a standard deviation of 28.7.  Can you conclude that the mean size is different between the two diet regimes?  Conduct a two tailed hypothesis test using alpha = .05.    f

Problem 4: Determine the correct answer from the UPPER CASE choices. Let the null hypothesis be that all people charged with a crime are considered innocent until proven guilty.

4a: A person is guilty, but the jury finds him innocent. This is an example of a TYPE I/TYPE II error. 

4b: A person is innocent, but the jury finds him guilty. This is an example of a TYPE I/TYPE II error.