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.

a. ( h_0: sigma^2
eq 1.14 ) ( h_a: sigma^2 = 1.14 ) (claim) b. ( h_0: sigma^2 geq 1.14 ) ( h_a: sigma^2 < 1.14 ) (claim)
c. ( h_0: sigma^2 leq 1.14 ) (claim) ( h_a: sigma^2 > 1.14 ) d. ( h_0: sigma^2 = 1.14 ) (claim) ( h_a: sigma^2
eq 1.14 )

(b) find the critical value(s) and identify the rejection region(s).
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 < square ) and ( chi^2 > square ).
c. the rejection region is ( chi^2 < square ).

Explanation:

1. Hypothesis Type: The alternative hypothesis $H_{a}: \sigma^{2}

eq 1.14$ indicates a two - tailed test. In a two - tailed chi - square test for variance, there are two rejection regions: one in the left tail and one in the right tail of the chi - square distribution.

1. Critical Values and Rejection Regions: We have two critical values, 13.09 (left - tail critical value) and 35.17 (right - tail critical value). For a two - tailed test, the rejection regions are $\chi^{2}<\text{left - tail critical value}$ and $\chi^{2}>\text{right - tail critical value}$. So the rejection regions are $\chi^{2}<13.09$ and $\chi^{2}>35.17$.

Answer:

B. The rejection regions are $\chi^{2} < 13.09$ and $\chi^{2} > 35.17$.