Question

a snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.14. a dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.14. at α = 0.10, is there enough evidence to reject the manufacturer’s claim? assume the population is normally distributed. complete parts (a) through (e) below.

(a) write the claim mathematically and identify h₀ and hₐ.

a. h₀: σ² ≠ 1.14
hₐ: σ² = 1.14 (claim)

b. h₀: σ² ≥ 1.14
hₐ: σ² < 1.14 (claim)

c. h₀: σ² ≤ 1.14 (claim)
hₐ: σ² > 1.14

d. h₀: σ² = 1.14 (claim)
hₐ: σ² ≠ 1.14

Explanation:

The manufacturer's claim is that the variance (\(\sigma^2\)) of carbohydrates in servings is 1.14. In hypothesis testing, the null hypothesis (\(H_0\)) typically contains the claim being tested (when it's a two - tailed or a claim of equality). Here, the claim is about the variance being equal to 1.14, so \(H_0:\sigma^2 = 1.14\) (with this as the claim). The alternative hypothesis (\(H_a\)) is the complement of the null hypothesis when we are testing if there is enough evidence to reject the claim. Since we are testing if the variance is different from 1.14 (a two - tailed test in this context as we just want to see if there's evidence to reject the claim of variance = 1.14), \(H_a:\sigma^2
eq1.14\). Options A, B, and C do not correctly represent the claim and the null/alternative hypotheses as A has the claim in the alternative, B and C have incorrect claims in the null.

Answer:

D. \( H_0: \sigma^2 = 1.14 \) (Claim)
\( H_a: \sigma^2
eq 1.14 \)