8-6 p421 n11
Original claim: peanut M&M candies have weights that vary more than the weights of plain M&M candies, e.g. the standard deviation of the weights of peanut M&M candies is more than 0.056 grams, the standard deviation of plain M&M candies
σ > 0.056

The Null Hypothesis
H₀: σ = 0.056

The Alternate Hypothesis
H₁: σ > 0.056

A sample of n = 41 has 40 degrees of freedom.
For a right tailed test and a level of significance, α = 0.01
χ²_critical = 63.691

Data:
s = 0.31
χ²_test = (41-1)×0.31²/0.056² = 1225.765

Because 1225.765 is IN the Critical Region, we Reject the Null Hypothesis and the statistical analysis of the data can support the original claim.

Conclusion:
The sample data SUPPORT the claim that peanut M&M candies have weights that vary more than the weights of plain M&M candies, e.g. the standard deviation of the weights of peanut M&M candies is more than 0.056 grams, the standard deviation of plain M&M candies