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: X2=(n−1)s2σ2X^2=\frac{(n-1)s^2}{\sigma ^2}
nn: sample size
ss: sample standard deviation
σ\sigma: population standard deviation
(n−1)(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?
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10.
Hypothesis Testing
10.1
Null hypothesis and alternative hypothesis
10.2
Proving claims
10.3
Confidence levels, significance levels and critical values
10.4
Test statistics
10.5
Traditional hypothesis testing
10.6
P-value hypothesis testing
10.7
Mean hypothesis testing with t-distribution
10.8
Type 1 and type 2 errors
10.9
Chi-Squared hypothesis testing
10.10
Analysis of variance (ANOVA)
10.11
Chi-square goodness of fit test
Statistics