Question

A manufacturer of a specific pesticide useful in control of household insects claims that after six months on the shelf, the variance of the amount of active ingredient among cans is no more than 4 grams2. A consumer group obtained a random sample of 20 recently produced cans of the pesticide from the manufacturer. The cans were stored for 6 months and then individually tested for the amount of active ingredient. The sample variance of the 20 cans was 6.2 grams2. a. Is there sufficient evidence to indicate that the population variance of active ingredient has more variability after 6 months than that claimed by the manufacturer? Use α=.05. b. To what population does your conclusion formally apply? What distributional assumptions must be made about the amount of active ingredient in a can of pesticide?

Answer 1

The answers of the questions are given in subparts as given in the question.It is a problem of one sample variance test where mean(miu) is not given.

At first we are to answer the question given in part b,i.e about the assumption of the distribution.

b)

The value of chi-sq(0.05,19) is calculated from the table 8 of Biometrika tables for statisticians vol-1.