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 1.11. At alpha equals 0.05​, 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 Upper H 0 and Upper H Subscript a. A. Upper H 0​: sigma squaredequals1.14 ​(Claim) Upper H Subscript a​: sigma squarednot equals1.14 B. Upper H 0​: sigma squaredgreater than or equals1.14 Upper H Subscript a​: sigma squaredless than1.14 ​(Claim) C. Upper H 0​: sigma squaredless than or equals1.14 ​(Claim) Upper H Subscript a​: sigma squaredgreater than1.14 D. Upper H 0​: sigma squarednot equals1.14 Upper H Subscript a​: sigma squaredequals1.14 ​(Claim) ​(b) Find the critical​ value(s) and identify the rejection​ region(s). The critical​ value(s) is(are) nothing. ​(Round to three 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 regions are chi squaredless than nothing and chi squaredgreater than nothing. B. The rejection region is chi squaredgreater than nothing. C. The rejection region is chi squaredless than nothing. ​(c) Find the standardized test statistic chi squared. nothing ​(Round to three 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. ▼ Fail to reject Reject Upper H 0. There ▼ is is not enough evidence to at the 5​% 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.

Answer 1

(a)

(b)  The tests statistics will follow a chi-square distribution with n-1= 23 degrees of freedom. Thus, for a two-tailed test, at alpha equals 0.05, the critical values are 11.698, 38.076.

A. The rejection regions are chi squared less than 11.698 and chi squared greater than 38.076.

(c) The test statistics is given by

(d)  As the test statistics does not lie in the rejection region, thus we fail to reject the null hypothesis.

(e)

Fail to reject H₀. There is not enough evidence to at the 5​% 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.