1. Chi Square Goodness-of-Fit
An ABC News Poll asked adults whether they felt that genetically modified food was safe to eat.  35% said it was safe; 52% said that it was not safe;  and 13% had no opinion. The same question was given to a random sample  of 120 adults at the State Fair. At the fair, 40 people said that it was safe;  60 said that it was not safe; and 20 had no opinion. Is there evidence that State Fair attendees have a different opinion on the safety of genetically  modified food?

2. Chi Square Goodness-of-Fit
An ABC News Poll asked adults whether they felt that genetically modified food was safe to eat.  35% said it was safe; 52% said that it was not safe;  and 13% had no opinion. The same question was given to a random sample  of 120 adults at the State Fair. At the fair, 40 people said that it was safe;  60 said that it was not safe; and 20 had no opinion. Is there evidence that State Fair attendees have a different opinion on the safety of genetically  modified food?
Let’s organize this information with a table!

3. Chi Square Goodness-of-Fit
In order to test this, we are going to use hypothesis testing with the Chi Square Goodness-of-Fit (GOF) test.

4. Chi Square Goodness-of-Fit
We know that this shape is not constant since it depends on certain information, which means that we are going to use something that we saw last concept category: degrees of freedom.
For the Goodness of Fit test, df is the number of categories minus 1.
The higher the df, the closer the Chi Square model gets to the Normal model.

5. Chi Square Goodness-of-Fit
Typical hypothesis test:
H0: the actual distribution is the same as some given distribution HA: the actual distribution is not the same as some gi ven distribution Requirements:  
Random Sample*
All expected counts ≥ 5
Less than 10% of population
***Chi Square GOF tests are always one-tailed!

6. Chi Square Goodness-of-Fit

7. Chi Square Goodness-of-Fit
So now, let’s jump into testing our original example!

8. Chi Square Goodness-of-Fit
So now, let’s jump into testing our original example!
We’ll start by putting our information in a list, and then the expected values in another list.