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July 29, 2016
Posted by **Tom E.** on Sunday, September 14, 2008 at 10:45pm.

Of those who earn less than $20,000, 9 are self-employed, 12 are employed by small firms, 40 by medium size firms, and 89 by large firms.

Of those who earn $20,000 to $39,999, 11 are self-employed, 10 are employed by small firms, 45 by medium size firms, and 104 by large firms.

Of those who earn $40,000 or more, 10 are self-employed, 13 are employed by small firms, 50 by medium size firms, and 107 by large firms.

Using the .05 level of significance, use a chi-square test to test the hypothesis that there is no relationship between the income level of the industrial salespeople and their employment status. Be sure to state the critical value, the test statistic value, and your interpretation of the test results.

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**PsyDAG**, Monday, September 15, 2008 at 3:09amNeed to complete your question. Repost with all of the data. If you used copy and paste, this does not seem to work. Carefully type the data.

I hope this helps. Thanks for asking.- statistics -
**Tom E.**, Monday, September 15, 2008 at 11:49amSorry for the lost of info...

A survey of industrial salespeople who are either self-employed, work for small, medium-sized, or large firms revealed the following with respect to incomes:

Of those who earn less than $20,000, 9 are self-employed, 12 are employed by small firms, 40 by medium size firms, and 89 by large firms.

Of those who earn $20,000 to $39,999, 11 are self-employed, 10 are employed by small firms, 45 by medium size firms, and 104 by large firms.

Of those who earn $40,000 or more, 10 are self-employed, 13 are employed by small firms, 50 by medium size firms, and 107 by large firms.

Using the .05 level of significance, use a chi-square test to test the hypothesis that there is no relationship between the income level of the industrial salespeople and their employment status. Be sure to state the critical value, the test statistic value, and your interpretation of the test results.- statistics -
**Tom E.**, Monday, September 15, 2008 at 11:50amSorry for the lost info....

A survey of industrial salespeople who are either self-employed, work for small, medium-sized, or large firms revealed the following with respect to incomes:

Of those who earn less than $20,000, 9 are self-employed, 12 are employed by small firms, 40 by medium size firms, and 89 by large firms.

Of those who earn $20,000 to $39,999, 11 are self-employed, 10 are employed by small firms, 45 by medium size firms, and 104 by large firms.

Of those who earn $40,000 or more, 10 are self-employed, 13 are employed by small firms, 50 by medium size firms, and 107 by large firms.

Using the .05 level of significance, use a chi-square test to test the hypothesis that there is no relationship between the income level of the industrial salespeople and their employment status. Be sure to state the critical value, the test statistic value, and your interpretation of the test results.

Thanks for the help!- statistics -
**Tom E.**, Monday, September 15, 2008 at 11:53amThis is driving me crazy!!!

A survey of industrial salespeople who are either self-employed, work for small, medium-sized, or large firms revealed the following with respect to incomes: Of those who earn less than $20,000, 9 are self-employed, 12 are employed by small firms, 40 by medium size firms, and 89 by large firms. Of those who earn $20,000 to $39,999, 11 are self-employed, 10 are employed by small firms, 45 by medium size firms, and 104 by large firms. Of those who earn $40,000 or more, 10 are self-employed, 13 are employed by small firms, 50 by medium size firms, and 107 by large firms. Using the .05 level of significance, use a chi-square test to test the hypothesis that there is no relationship between the income level of the industrial salespeople and their employment status. Be sure to state the critical value, the test statistic value, and your interpretation of the test results.

I had to make it one big paragraph.

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**MathGuru**, Monday, September 15, 2008 at 9:33pmTo find expected values for each cell, here is a formula you can use:

E = (row total)(column total)/n

...where E is the expected cell count if the null hypothesis is true.

The null hypothesis states the variables are unrelated in the population. The alternate or alternative hypothesis states the variables are related in the population. The purpose of a chi-square test is to determine if two or more variables are independent of each other (the null hypothesis) or are dependent (the alternate or alternative hypothesis). If the null is rejected, you can conclude that the variables are related in some manner or connected in some way. If the null is not rejected, you cannot conclude that the variables are related.

To calculate the chi-square statistic (after you have your expected values), you can use a formula like the following:

Chi sq = the sum of [(O - E)^2/E]

...where ^2 means squared.

(Take each cell, subtract the expected value from the observed value, square it, then divide by the expected value. Do this for each cell. Then add all the values together for the chi-square statistic.)

Using a table for critical or cutoff values for the chi-square (usually found in the appendix section of a statistics textbook), find the critical value using .05 level with degrees of freedom. Degrees of freedom = (r - 1)(c - 1) ...where r = number of rows and c = number of columns. If your test statistic exceeds the critical value from the table, then the null is rejected. If your test statistic does not exceed the critical value from the table, then the null is not rejected.

I hope this will help get you started.