Question

To prevent E. coli, meat should be cooked to an internal temperature of at least 160°F. However, different meat patties cooked for the same amount of time will have different final internal temperatures because of variations in the patties and variations in burner temperatures. A regional hamburger chain plans to replace its current burners with one of two new digitally controlled models. If there is a significant difference in the variance of the two models, the chain will select the model with the smaller variance in the final internal meat temperature. The chain's purchasing directors have arranged to randomly sample 11 patties cooked by burner model 1 and 13 cooked by burner model 2. Perform a hypothesis test at the 10% significance level to see whether there is a significant difference between the variances of the two burner models. Model 1 Model 2 1 180.0 178.6 2 181.5 182.3 3 178.9 177.5 4 176.4 180.6 5 180.7 178.3 6 181.0 180.7 7 180.3 181.4 8 184.6 180.5 9 185.6 179.6 10 179.7 178.2 11 178.9 182.0 12 181.5 13 180.8

Answer 1

First of all we find the sample standard deviation for both Models

Let S₁² denote the sample variance for Model 1

Let S₂² denote the sample variance for Model 2

We compute the sample variance using the formula :

We get :

Also,

Sample size for Model 1 = n₁ = 11

Sample size for Model 2 = n₂ = 13

Now,

We conduct F-test for the Equality of Two Population Variances as :

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Hence, there is not enough evidence to conclude that there is a significant difference between the variances of the two burner models.