The highway department is testing two types of reflecting paint for concrete bridge end pillars. The two kinds of paint are alike in every respect except that one is orange and the other is yellow. The orange paint is applied to 12 bridges, and the yellow paint is applied to 12 bridges. After a period of 1 year, reflectometer readings were made on all these bridge end pillars. (A higher reading means better visibility.) For the orange paint, the mean reflectometer reading was x̅₁ = 9.4, with standard deviation s₁ = 2.1.

For the yellow paint, the mean was x̅₂ = 6.9, with standard deviation s₂ = 2.0.

Based on these data, can we conclude that the yellow paint has less visibility after 1 year? (Use a 1% level of signi­ficance.)

(a) What is the level of signifi­cance? State the null and alternate hypotheses.

(b) What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic and corresponding distribution value.

(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically signifi­cant at level a?

(e) Interpret your conclusion in the context of the application.

For degrees of freedom d.f. not in the Student’s t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more “conservative” answer. Answers may vary due to rounding.