The owners of a motel discovered that a defective product was used during construction. It took seven months to correct the defects during which approximately 14 rooms in the 100 -unit motel were taken out of service for one month at a time. The data are in the file motel.

a. Calculate the sample average occupancy rate for the motel during the time when there were no repairs being made. What is the sample average occupancy rate for the motel during the time when there were repairs being made? How big a difference is there?

b. Consider the linear regression MOTEL_PCT \(=\delta_{1}+\delta_{2}\) REPAIR \(+e\), where REPAIR is an indicator variable taking the value 1 during the repair period and 0 otherwise. What are the estimated coefficients? How do these estimated coefficients relate to the calculations in part (a)?

c. Construct a \(95 \%\) interval estimate for the parameter \(\delta_{2}\) and give its interpretation. Have we estimated the effect of the repairs on motel occupancy relatively precisely, or not? Explain.

d. The motel wishes to claim economic damages because the faulty materials led to repairs which cost them customers. To do so, their economic consultant tests the null hypothesis \(H_{0}: \delta_{2} \geq 0\) against the alternative hypothesis \(H_{1}: \delta_{2}<0\). Explain the logic behind stating the null and alternative hypotheses in this way. Carry out the test at the \(\alpha=0.05\) level of significance. Discuss your conclusions. Clearly state the test statistic, the rejection region, and the \(p\)-value.

e. To further the motel's claim, the consulting economist estimates a regression model \(\left(M O T E L \_P C T-C O M P \_P C T\right)=\gamma_{1}+\gamma_{2}\) REPAIR \(+e\), so that the dependent variable is the difference in the occupancy rates. Construct and discuss the economic meaning of the \(95 \%\) interval estimate of \(\gamma_{2}\).

f. Test the null hypothesis that \(\gamma_{2}=0\) against the alternative that \(\gamma_{2}<0\) at the \(\alpha=0.01\) level of significance. Discuss the meaning of the test outcome. Clearly state the test statistic, the rejection region, and the \(p\)-value.