Question

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

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.

(c) use the $\chi^2$-test to find the standardized test statistic.
(round to three decimal places as needed.)

Explanation:

Step1: Recall the formula for the chi - square test statistic for standard deviation

The formula for the chi - square test statistic \(\chi^{2}=\frac{(n - 1)s^{2}}{\sigma^{2}}\), where \(n\) is the sample size, \(s\) is the sample standard deviation, and \(\sigma\) is the population standard deviation.

Step2: Identify the values

We are given that \(n = 41\), \(s=0.28\), and \(\sigma = 0.331\).

Step3: Calculate \((n - 1)\)

First, calculate \(n-1\): \(n - 1=41-1 = 40\).

Step4: Calculate \(s^{2}\) and \(\sigma^{2}\)

\(s^{2}=(0.28)^{2}=0.0784\) and \(\sigma^{2}=(0.331)^{2}=0.109561\).

Step5: Substitute the values into the formula

\(\chi^{2}=\frac{(40)\times(0.0784)}{0.109561}=\frac{3.136}{0.109561}\approx30.765\)

Answer:

30.765