A Local School District Is Concerned About the Number of School

A local school district is concerned about the number of school days missed by its teachers due to illness. A
random sample of 10 teachers is selected. The number of days absent in one year is listed below. An incentive
program is offered in an attempt to decrease the number of days absent. The number of days absent in one year
after the incentive program is listed below. Test the claim that the incentive program cuts down on the number
of days missed by teachers. Assume the samples are random and dependent, and the populations are normally
distributed. Use $\alpha = 0.05 .$ $$\begin{array} { l | c | c | c | c | c | c | c | c | c | c | } \text { Teacher } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } & \text { I } & \text { J } \\\hline \begin{array} { l } \text { Days absent before } \\\text { incentive }\end{array} & 3 & 8 & 7 & 2 & 9 & 4 & 2 & 0 & 7 & 5 \\\hline\begin{array} { l } \text { Days absent after } \\\text { incentive }\end{array} & 1 & 7 & 7 & 0 & 8 & 2 & 0 & 1 & 5 & 5 \\\end{array}$$