# Chi-square goodness of fit cannot find expected values

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1. Apr 30, 2017

### Rifscape

1. The problem statement, all variables and given/known data
An article in Business Week reports profits and losses of firms by industry. A random sample of 100 firms is selected, and for each firm in the sample, we record whether the company made money or lost money, and whether or not the firm is a service company. The data are summarized in the 2×2 table below. Use a 10% level of significance to test whether the two events "the company made profit this year" and "the company is in the service industry" are independent.

Industry Type

Service Nonservice

Profit 35 36

Loss 12 17

I am not sure how to find the expected values, any advice is appreciated

2. Relevant equations

Chi-squre = ∑(O-E)^2/E
3. The attempt at a solution

I am not sure how to find the expected values, if someone can tell me how to find those, I will be able to solve the problem.

I'm not sure how to find the expected value when given a table bigger than 1 x n, if someone could explain how to do this it would be much appreciated.

Any help would be greatly appreciated, thanks

2. Apr 30, 2017

### FactChecker

The relevant equation that you have not listed is the definition of independent events. Write that down and fill in as much as you can from the data you have.

3. Apr 30, 2017