Chapter 12, Problem 35SE

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

Number of Sales	Observed Frequency (days)
0	30
1	32
2	25
3	10
4	3
Total	100

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 probability distribution. The binomial probability function presented in Chapter 5 is

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

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.

• 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 probability distribution should be rejected. Use α = .05. Because no parameters of the binomial probability distribution were estimated from the sample data, the degrees of freedom are k − 1 when k is the number of categories.