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# Expected Frequencies and Goodness of Fit Test

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

Number of Sales
0
1
2
3
4

Observed Frequency
30
32
25
10
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 distribution.

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 alpha = .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.