Chi Square Testing, Would GREATLY Appreciate Review of My Work + Help

2. Using the following data, test the question that an equal number of Democrats, Republicans, and Independents voted during the most recent election. Test the hypothesis at the .05 level of significance. Do this by hand.

**Political Affiliation** |

Republican | Democrat | Independent |

800 | 700 | 900 |

x^{2 = e (observed value-expected value)2/Expected Value}

N=3, DF=2

1) 800 + 700 + 900 = 2400/3 (N)= "800"

2) Observed Data = -100, 0, 100

3) Expected Data = 800

4) (0)2/800 = 0, (-100)2/800 = 12.5, (100)2/800 = 12.5, therefore 12.5 + 12.5 = __25__

5) Reffering to chi square table, with two degrees of freedom at .025, distribution is 7.378

6) 25>7.278, therefore **REJECT the hypothesis**

Conclusion: Reject the hypothesis, political affiliation participation varies by category.

3. School enrollment officials expected a change in the distribution of the number of students across grades and were not sure whether it is what they should have expected. Test the following data for goodness of fit at the .05 level.

^{Grade} | ^{1} | ^{2} | ^{3} | ^{4} | ^{5} | ^{6} |

^{Number of students} | ^{309} | ^{432} | ^{346} | ^{432} | ^{369} | ^{329} |

^{x2 = e (observed value-expected value)2/Expected Value}

^{Sum of Students: 2217}

^{N=6, DF= 5}

This is where I am completely lost...I can't figure out what the expected values are and it feels completely different than the last, can somebody help me?

Re: Chi Square Testing, Would GREATLY Appreciate Review of My Work + Help

Hey irizavrima.

Q2 looks very good. For Q3 you will have to make some kind of assumption about grade distribution.

The assumptions for grade distribution vary on the course offering, past history and other factors that can affect the distribution of grades. For example a course in Quantum ChromoDynamics will have a distribution that is a lot different to say a course in introductory economics.

When you figure out the assumptions to get the expected distribution or just obtain the expected distribution (through some argument) then you can do the chi-square test and obtain a test-statistic to test your hypothesis.

I don't think a uniform grade would a good assumption, but perhaps a Normally distributed grade curve or a skewed normal (like a Beta distribution) can be used.

If these are used then you will need to "bin" the distribution by dividing it into 6 even regions and get the probability (or rather the frequency) for each region where frequency is calculated by using frequency = probability * Number_Of_Students.