Question

Highway engineers in Ohio are painting white stripes on a highway. The stripes are supposed to be approximately 10 feet long. However, because of the machine, the operator, and the motion of the vehicle carrying the equipment, considerable variation occurs among the stripe lengths. Engineers claim that the variance of stripes should be less than 16 inches squared. At α = .05, use the sample lengths given here from 12 measured stripes (in feet and inches) to test the variance claim. Assume stripe length is normally distributed. Interpret your result.

(in feet)	(in inches)
9.85	118.2
9.7	116.4
9.9	118.8
9.5	114
9.15	109.8
10.1	121.2
10	120
9.8	117.6
9.9	118.8
10.3	123.6
10.1	121.2
10.2	122.4

                        

            

                                    

E1.      The appropriate test for this question is:

            a.         a Z-test for the true variance of stripe length.

            b.         a t-test for the true mean of stripe length.

            c.         a Chi-square test for the true mean of stripe length.

            d.         a Chi-square test for the true variance of stripe length.

E2.      The appropriate test to answer the question about the claim should be:

            a.         a right-hand-side tailed test.

            b.         a left-hand-side tailed test.

            c.         a two-tailed test.

            d.         Can’t decide.

E3.      The p-value for this test is 0.46687. Is the claim that the stripe length is less than 16 inches squared true or not, at 5% level of significance?

            a.         True.

            b.         Data evidence does not support the claim.

            c.         Don’t know.

            

            

            

Answer 1

E1. The correct answer is option D. For a normally distributed variable, chi-squared test statistic helps in determining whether the sample and population variances are the same or not.

E2. The correct answer is option B. Since the claim says that the variance of stripes should be less than 16 inches squared, it refers to the area under the normal curve which lies to the left of 16, and is the critical region for rejection/acceptance of the claim.

E3. Since the p-value for this test is greater than the significance level of 5% (0.05), we do not reject the null hypothesis/claim in this scenario. Thus, we can say that the claim appears to be true. Option A is the correct answer.