# Chi-Squared hypothesis testing

### Chi-Squared hypothesis testing

#### Lessons

If a claim is made about population variance, we can test this claim using our sample variance using a Chi-Squared distribution,

• Chi-Squared: $X^2=\frac{(n-1)s^2}{\sigma ^2}$
$n$: sample size
$s$: sample standard deviation
$\sigma$: population standard deviation
$(n-1)$: is also called "degrees of freedom"
• Chi-Square table gives critical value area to the right
• Introduction
What is Chi-Squared Hypothesis Testing?

• 1.
Variance Hypothesis Testing
A sample of 10 dumbbells is weighted. The variance of this sample is 25 grams. With a 90% confidence level what can be said about the following claims:
a)
"The variance of all dumbbells is equal to 15 grams"

b)
"The variance of all dumbbells is more than 15 grams"

• 2.
Bertie Bott's Every Flavour Beans are on average 2.35 grams. The manufactures (Bertie & Bill Bott) sample 26 beans, and it is found that their standard deviation is 0.043 grams. With a 95% confidence level can Bertie Bott's say that their beans have a standard deviation of less than 0.05 grams?