Chi-Squared hypothesis testing

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  1. 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:
    1. "The variance of all dumbbells is equal to 15 grams"
    2. "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?
    Topic Notes
    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=(n1)s2σ2X^2=\frac{(n-1)s^2}{\sigma ^2}
    nn: sample size
    ss: sample standard deviation
    σ\sigma: population standard deviation
    (n1)(n-1): is also called "degrees of freedom"
    • Chi-Square table gives critical value area to the right