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 manufacturers claim? assume the population is normally distributed. complete parts (a) through (e) below.

the critical value(s) is(are) 13.09, 35.17.
(round to two decimal places as needed. use a comma to separate answers as needed.)
choose the correct statement below and fill in the corresponding answer boxes.

a. the rejection region is \\(\chi^2 > \square\\).

b. the rejection regions are \\(\chi^2 < 13.09\\) and \\(\chi^2 > 35.17\\).

c. the rejection region is \\(\chi^2 < \square\\).

(c) find the standardized test statistic \\(\chi^2\\).
22.99 (round to two decimal places as needed.)
(d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. fill in the correct answers below.
\\(\boldsymbol{h_0}\\). there \\(\boldsymbol{\square}\\) enough evidence to at the 10% level of significance to reject the manufacturers claim that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.14.

Explanation:

Step1: Recall the rejection regions

The rejection regions are \( \chi^2 < 13.09 \) and \( \chi^2 > 35.17 \) (from part (b)).

Step2: Compare test statistic with rejection regions

The standardized test statistic \( \chi^2 = 22.99 \). We check if \( 22.99 \) is in the rejection regions. Since \( 13.09 < 22.99 < 35.17 \), the test statistic is not in the rejection regions.

Step3: Make a decision about \( H_0 \)

If the test statistic is not in the rejection region, we fail to reject the null hypothesis \( H_0 \). This means there is not enough evidence at the \( \alpha = 0.10 \) level of significance to reject the manufacturer's claim.

Answer:

Fail to reject \( H_0 \). There is not enough evidence to at the 10% level of significance to reject the manufacturer’s claim that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.14.