Chi-square goodness of fit cannot find expected values

In summary: A good start would be to contrast the observed values with the expected values, and that would require some knowledge of the conditions under which the chi-square test is appropriate.In summary, the conversation discusses the use of a 2x2 table to test whether the events "the company made profit this year" and "the company is in the service industry" are independent. A chi-square test is mentioned, but the participants are unsure of how to find the expected values for the test. They ask for advice and resources to help them solve the problem.
  • #1
Rifscape
41
0

Homework Statement


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

Homework Equations



Chi-squre = ∑(O-E)^2/E

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[/B]
 
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  • #2
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
Rifscape said:

Homework Statement


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

Homework Equations



Chi-squre = ∑(O-E)^2/E

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[/B]
Google is your friend: try "chi-square test", for example. Alternatively: look in your textbook.
 

What is Chi-square goodness of fit?

Chi-square goodness of fit is a statistical test used to determine whether observed data fits a certain theoretical distribution. It is often used to compare expected values, which are calculated based on a theoretical model, to actual observed values in a dataset.

Why can't Chi-square goodness of fit find expected values?

Chi-square goodness of fit cannot find expected values if the observed data does not fit the theoretical distribution. This can happen if there is a large discrepancy between the expected and observed values, or if there is a small sample size.

What does it mean if Chi-square goodness of fit cannot find expected values?

If Chi-square goodness of fit cannot find expected values, it means that there is a significant difference between the observed and expected values. This could indicate that the observed data does not follow the expected distribution, or that there is some other underlying factor affecting the data.

Can Chi-square goodness of fit still be used if it cannot find expected values?

Yes, Chi-square goodness of fit can still be used even if it cannot find expected values. However, the results should be interpreted with caution as the test may not accurately reflect the fit of the data to the theoretical distribution.

How can I improve my Chi-square goodness of fit test if it cannot find expected values?

If Chi-square goodness of fit cannot find expected values, it may be helpful to increase the sample size or adjust the expected values to better fit the observed data. It may also be beneficial to check for any errors in the data or re-evaluate the chosen theoretical distribution.

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