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. $h_0: \sigma \leq 0.331$; $h_a: \sigma > 0.331$ (claim) b. $h_0: \sigma \geq 0.331$ (claim); $h_a: \sigma < 0.331$ c. $h_0: \sigma = 0.331$; $h_a: \sigma \
eq 0.331$ (claim) (b) find the critical value(s). 59.342 (use a comma to separate answers as needed. round to three decimal places as needed.) identify the rejection region(s). a. b. c.

Explanation:

Step1: Identify Test Type

This is a chi - square test for population standard deviation (or variance). The claim is that the standard deviation of peanut candies' weights ($\sigma$) is greater than that of plain candies ($\sigma_0 = 0.331$), so it's a right - tailed test.

Step2: Determine Degrees of Freedom

The sample size $n = 41$. For a chi - square test of standard deviation, the degrees of freedom $df=n - 1$. So $df=41 - 1=40$.

Step3: Find Critical Value

We are using a significance level $\alpha = 0.025$ for a right - tailed test. We look up the critical value in the chi - square distribution table with $df = 40$ and $\alpha=0.025$. From the chi - square table (or using statistical software/calculator), the critical value $\chi^2_{0.025,40}=59.342$.

Answer:

59.342