Question

a snack food manufacturer estimates that the variance of the number of grams of carbohyd chips is 1.37. a dietician is asked to test this claim and finds that a random sample of 19 se 1.36. at α = 0.10, is there enough evidence to reject the manufacturers claim? assume the distributed. complete parts (a) through (e) below.
(a) write the claim mathematically and identify h₀ and hₐ.
a. h₀: σ² ≥ 1.37
hₐ: σ² < 1.37 (claim)

b. h₀: σ² ≤ 1.37 (claim)
hₐ: σ² > 1.37

c. h₀: σ² = 1.37 (claim)
hₐ: σ² ≠ 1.37

d. h₀: σ² ≠ 1.37
hₐ: σ² = 1.37 (claim)

Explanation:

The manufacturer claims the variance of the number of grams of carbohydrate in chips is 1.37. In hypothesis testing, the null hypothesis \(H_0\) usually contains the claim (when the claim is a specific value or equality - related). The alternative hypothesis \(H_a\) is the complement. So the claim is \(H_0:\sigma^{2}=1.37\) (claim), and \(H_a:\sigma^{2}
eq1.37\) (since we are testing if there's evidence to reject the claim, the alternative is a two - tailed test of inequality). Option C has \(H_0:\sigma^{2} = 1.37\) (Claim) and \(H_a:\sigma^{2}
eq1.37\), which matches this.

Answer:

C. \(H_0:\sigma^{2}=1.37\) (Claim) \(H_{a}:\sigma^{2}
eq1.37\)