Project 45: Chi Square GOF

Intro Problem: A school administrator believes that the distribution of student grade levels are as follows:

9th Grade: 35%

10th Grade: 30%

11th Grade: 20%

12th Grade: 15%

To test the claim at the .05 level, she randomly samples a group of students from the school and obtains the following:

9th graders: 60

10th graders: 50

11th graders: 40

12th graders: 30

Explanation:

Ho: p9 = .35, p10 = .3, p11 = .2, p12 = .15 (model)

Ha: the model posed is not a good fit

n = 60 + 50 + 40 + 30 = 180

Expected Counts: 180(.35) = 63, 180(.3) = 54, 180(.2) = 36, 180(.15) = 27

Chi Square Test Statistic: (60-63)^2/63 + (50-54)^2/54 + (40-36)^2/36 + (30-27)^2/27 = 1.22

Degrees of Freedom = number of categories - 1 = 4 - 1 = 3

pValue = .75  (which is the probability that a chi square value is greater than 1.22 with 3 degrees of freedom)

Since .75 > .05 we would fail to reject Ho and not get evidence that the administrator's claim is incorrect.

Project 45: The variables 'model' and 'counts' have been initialized.  There is also a working method called chicdf.

model represents the distribution of expected proportions ([.35, .3, .2, .15] in the example above)

counts represents the actual counts observed ([60, 50, 40, 30] in the example above)

chicdf(low, high, df) returns the probability that a chi square value is between low and high (with 'df' degrees of freedom)

Task: Appropriately initialize the values of 'chi' and 'pValue' that represents the chi square test statistic and the p-value for the goodness of fit test.

**If your code works for 5 test cases, you can enter your e-mail address

Universal Computational Math Methods:

pow(5,2) returns 25.0

abs(-3.0) returns 3

sqrt(49.0) returns 7.0