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 ( h_0 ) and ( h_a ).

\\( \bigcirc \\) a. ( h_0: \sigma \leq 0.331 ); ( h_a: \sigma > 0.331 ) (claim)
\\( \bigcirc \\) b. ( h_0: \sigma \geq 0.331 ) (claim); ( h_a: \sigma < 0.331 )
\\( \bigcirc \\) c. ( h_0: \sigma = 0.331 ); ( h_a: \sigma \
eq 0.331 ) (claim)

Explanation:

The claim is that peanut candies have weights that vary more than plain candies. Variation is measured by standard deviation (\(\sigma\)). The standard deviation of plain candies is 0.331, so "vary more" means \(\sigma\) (for peanut candies) is greater than 0.331. The null hypothesis (\(H_0\)) is the statement of no effect or the opposite of the claim (or equality/inequality that includes the claim's opposite), and the alternative hypothesis (\(H_a\)) is the claim. So \(H_0\) should be \(\sigma \leq 0.331\) (saying peanut candies do not vary more or vary the same) and \(H_a\) is \(\sigma > 0.331\) (the claim that they vary more). Option A matches this.

Answer:

A. \( H_0: \sigma \leq 0.331 \); \( H_a: \sigma > 0.331 \) (Claim)