Chi-squared

=**Chi Square in a nutshell:**=


 * Significance level:** Given on examinations, either 1%, 5%, or 10%.


 * Null Hypothesis Ho:** The variables are independent.


 * Alternative Hypothesis H1:** The variables are not independent.


 * Degrees of Freedom:** (# rows – 1)(# columns – 1)


 * Expected Frequencies:** (row total)(column total) / (grand total)

A) compare χ2 calc to χ2 crit __**OR**__
 * Conclusion: O**ne of two ways.

B) compare //p//-value to significance level


 * A) Critical Value:** use table with degrees of freedom and significance level
 * Chi Square Calculated value:** Σ ((O – E)2/E)
 * Conclusion:** If χ2 calc > χ2 crit, then reject Ho


 * B) //p//-value:** found on GDC
 * Conclusion:** If //p//-value < significance level then reject Ho

Elementary, Junior High, and Senior High student's grades were observed and recorded. The information is shown below. State an appropriate null hypothesis, compute the value of chi square, and test the null hypothesis at the 0.05 level.
 * Example**


 * || **Elementary** || **Junior High** || **Senior High** ||
 * **A or B** || 100 || 80 || 120 ||
 * **C** || 130 || 90 || 110 ||
 * **D or F** || 60 || 30 || 20 ||

1) State the null and alternative hypotheses.

2) Find the degrees of freedom.

3) Find the chi square critical value.

4) Find the expected frequencies.

5) Make a conclusion and justify (be sure to include a diagram) your results using: a) Chi square calculated value and critical value.

b) //p//-value and significance level.