45. A salesperson makes four calls per day. A sample of 100 days gives the following frequencies of sales volumes.

Records show sales are made to 30% of all sales calls. Assuming independent sales calls, the number of sales per day should follow a binomial distribution. The binomial probability function presented in Chapter 5 is For this exercise, assume that the population has a binomial distribution with n  4, p  .30, and x  0, 1, 2, 3, and 4.

a. Compute the expected frequencies for x  0, 1, 2, 3, and 4 by using the binomial probability function. Combine categories if necessary to satisfy the requirement that the expected frequency is five or more for all categories.

b. Use the goodness of fit test to determine whether the assumption of a binomial distribution should be rejected. Use α  .05. Because no parameters of the binomial distribution were estimated from the sample data, the degrees of freedom are k 1 when k is the number of categories.