Chi-Square distribution is used to test whether or not two factors are independent or dependent. Chi square is a test of dependence or independence.
Chi-square distribution is not bimodal or level. It seems to be a skewed bell shape. Going with skewed.
As the degrees of freedom increase the symmetry of the graph increases.
It is skewed to the right, and since the random variable on which it is based is squared, it has no negative values. As the degrees of freedom increases, the probability density function begins to appear symmetrical in shape.
Chi Square and Hypothesis testing
See additional notes on Hypothesis testing.
Don’t need knowledge of population variation
Evaluates sample variances
http://people.richland.edu/james/lecture/m170/ch12-int.html (Chi squared distribution)
http://www.itl.nist.gov/div898/handbook/eda/section3/eda358.htm (Chi squared test for the variance)
Chi Square Examples
The Barnes Company manufactures a DVD player and claims that the mean number of hours of use before repairs are needed is 400, with a standard deviation of 10 hours. The specified variance, therefore, is σo2 = 102 = 100 hours2. A new company marketing representative suspects that the “before repair” variance is actually less than 100 hours2. To verify this, she tests nine machines and finds a sample mean of 410 hours and a standard deviation of 5.5. Is the sample variance statistically significantly less than the currently claimed variance? Use α = 0.05.
Six Sigma Black Belt Certification Chi Square Questions:
Question: The time for a fail-safe device to trip is thought to be a discrete uniform distribution from 1 to 5 seconds. To test this hypothesis, 100 tests are conducted with results as shown below.
On the basis of these data, what are the chi square (c2) value and the number of degrees of freedom (df)?
(A) (c2) value = 57.5, degrees of freedom = 4
(B) (c2) value = 57.5, degrees of freedom = 5
(C) (c2) value = 1,150.0, degrees of freedom = 4
(D) (c2) value = 1,150.0, degrees of freedom = 5
Answer: 57.7. and 4 degrees of freedom.
First we will figure out the degrees of freedom. It’s an easy way to eliminate half the answers on the page.
There are 5 rows and 2 columns in the chart.
Degrees of freedom = (rows -1) * (columns – 1) = (5-1) * ( 2 – 1) = 4* 1 = 4.
Now we’ll run the equation Chi Squared = X^2 = Σ (((o-E)^2 )/ E) = 100 / 20 + 25 / 20 + 900 / 20 + 25/20 + 100 / 20 = 1150 / 20 = 57.5