The owners of a motel discovered that a defective product was used during construction. It took 7 months to correct the defects during which approximately 14 rooms in the 100 -unit motel were taken out of service for 1 month at a time. The data are in the file motel.

a. Create a new variable, RELPRICE2 \(=100\) RELPRICE, which equals the percentage of the competitor's price charged by the motel in question. Plot RELPRICE2 against TIME. Compute the summary statistics for this variable. What are the sample mean and median? What are the minimum and maximum values? Does the motel in question charge more than its competitors for a room, or less, or about the same? Explain.

b. Consider a linear regression with \(y=M O T E L_{-} P C T\) and \(x=\) RELPRICE2. Interpret the estimated slope coefficient. Construct a \(95 \%\) interval estimate for the slope. Have we estimated the slope of the relationship very well? Explain your answer.

c. Construct a \(90 \%\) interval estimate of the expected motel occupancy rate if the motel's price is \(80 \%\) of its competitor's price. Do you consider the interval relatively narrow or relatively wide? Explain your reasoning.

d. Test the null hypothesis that there is no relationship between the variables against the alternative that there is an inverse relationship between them, at the \(\alpha=0.05\) level of significance. Discuss your conclusion. Be sure to include in your answer the test statistic used, the rejection region, and the \(p\)-value.

e. Test the hypothesis that for each percent higher for the relative price that the motel in question charges, it loses \(1 \%\) of its occupancy rate. Formulate the null and alternative hypotheses in terms of the model parameters, carry out the relevant test at the \(5 \%\) level of significance, and state your conclusion. Be sure to state the test statistic used, the rejection region, and the \(p\)-value.