Chapter 12, Problem 37SE

Testing If Daily Sales Obey a Binomial Probability Distribution. A salesperson makes four calls per day. A sample of 100 days gives the following frequencies of sales volumes.

Records show sales result from 30% of all sales calls. Assuming independent sales calls, the number of sales per day should follow a binomial probability distribution. The binomial probability function is

$f(x)=\frac{n!}{x!(n-x)!}{p}^x{(1-p)}^{n-x}$

For this exercise, assume that the population has a binomial probability distribution with n = 4, p = .30, and x = 0, 1, 2, 3, and 4.

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