Question

A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.29. A dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.47. At α-0.01, is there enough evidence to re ect the man facturer's daim? Assume the population is normally distributed. Complete parts (a) through (e) below.

(a) Write the claim mathematically and identify H0 and Ha.

Answer 1

a) Hypothesis :

Two tailed test.

Critical values :

Given ,

Degrees of freedom = n - 1 = 24 - 1 = 23

Left tail critical value is ,

       { Using Excel, =CHIINV(0.995 , 23 ) = 9.26 }

Right tail critical value is ,

       { Using Excel, =CHIINV(0.005 , 23 ) = 44.18 }

So , critical values are 9.26 , 44.18    

The rejection region for this two-tailed test is ,

Rejection region : { : < 9.26 or > 44.18 }

Test Statistic :

Where , is hypothesized population variance = 1.29

is sample variance = 1.47

n is sample size = n = 24

Decision about null hypothesis :

It is observed that = 9.26 < = 26.209 < = 44.19

So fail to reject null hypothesis.

Conclusion :

There is not enough evidence to reject the manufacturer's claim.