Question

use a 0.025 significance level to test the claim that peanut candies have weights that vary more than plain candies. the standard deviation for the weights of plain candies is 0.331. a sample of 41 peanut candies has weights with a standard deviation of 0.28. assume the population is normally distributed.

(a) write the claim mathematically and identify h₀ and hₐ.
a. h₀: σ ≤ 0.331; hₐ: σ > 0.331 (claim)
b. h₀: σ ≥ 0.331 (claim); hₐ: σ < 0.331
c. h₀: σ = 0.331; hₐ: σ ≠ 0.331 (claim)

(b) find the critical value(s).
(use a comma to separate answers as needed. round to three decimal places as needed.)

Explanation:

Step1: Identify Test Type and Parameters

This is a right - tailed chi - square test for population standard deviation (or variance). The significance level $\alpha = 0.025$, the sample size $n = 41$, so the degrees of freedom $df=n - 1=41 - 1 = 40$.

Step2: Find Critical Value

For a right - tailed chi - square test, we need to find the critical value $\chi_{\alpha,df}^2=\chi_{0.025,40}^2$. Using a chi - square distribution table or a statistical calculator, we look up the value corresponding to $\alpha = 0.025$ and $df = 40$. From the chi - square distribution, $\chi_{0.025,40}^2=59.342$.

Answer:

59.342