**Directions:** Complete the assignment on your own paper. Clearly label each answer. Your answers for this assignment must include reasons; simply stating the answer without justification will earn partial credit. (30 points)

1. Lacking a table of random numbers, Dan decided to use the last digits in a set of five-place tables of logarithms. The number of times each integer occurred in a sample of size *n* = 50 is given below. If the collection of last digits is random, then we would expect each integer to occur, on average, equally often.

Integer0123456789

Frequency8673571463

Do the observed frequencies meet this expectation? Perform the appropriate test and report your findings. Be sure to include all the necessary steps. (10 points)

2. An experiment in chicken breeding results in offspring having very curly, slightly curly, or normal feathers. If this is the result of a single gene system, then the proportions of offspring in the three phenotypes should be 0.25, 0.50, and 0.25 respectively. In one such experiment, 93 chickens were born. 20 had normal feathers, 50 had slightly curly feathers, and 23 had very curly feathers. Carry out a test to determine whether the genetic model seems to hold in this setting. (10 points)

3. The M&M/Mars Company reports that their Peanut Chocolate Candies are produced in the following distribution: 20 percent each of browns, yellows, reds and blues, and 10 percent each of greens and oranges. Joey bought a bag of Peanut Chocolate Candies and counted out the following distribution of colors: 12 brown, 7 yellow, 4 red, 8 blue, 13 green and 2 orange. Perform a goodness of fit test of the company’s reported distribution and report your results. (10 points)

Subject | Mathematics |

Due By (Pacific Time) | 07/29/2014 10:00 am |

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