The Manager of a Fast Food Restaurant Wants to Determine

Essay

The manager of a fast food restaurant wants to determine how sales in a given week are related to the number of discount vouchers (#) printed in the local newspaper during the week. The number of vouchers and sales ($000s) from 10 randomly selected weeks is given below with Excel regression output. $$\begin{array} { | c | c | } \hline \text { Number of vouchers } & \text { Sales } \\\hline 4 & 12.8 \\\hline 7 & 15.4 \\\hline 5 & 13.9 \\\hline 3 & 11.2 \\\hline 19 & 18.7 \\\hline 10 & 17.9 \\\hline 8 & 16.8 \\\hline 6 & 15.9 \\\hline 3 & 11.5 \\\hline 5 & 13.9 \\\hline\end{array}$$ $\begin{array}{|l|c|c|c|c|c|c|}\hline \text { SUMMARY OUTPUT } & & \\\hline & & \\\hline \text { RegressionStatistics } & & \\\hline \text { Multiple R } & 0.8524 & \\\hline \text { RSquare } & 0.7267 & \\\hline \text { Adjusted R Square } & 0.6925 & \\\hline \text { Standard Error } & 1.4301 & \\\hline \text { Observations } & 10 & \\\hline & & \\\hline \text { ANOvA } & & & & & & \\\hline & d f & S S & \text { MS } & F & \text { significance } F & \\\hline \text { Regression } & 1 & 43.4982 & 43.4982 & 21.2682 & 0.0017 & \\\hline \text { Residual } & 8 & 16.3618 & 2.0452 & & & \\\hline \text { Total } & 9 & 59.8600 & & & & \\\hline & & \\\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper 95\% } \\\hline \text { Intercept } & 11.5676 & 0.8341 & 13.6579 & 0.0000 & 9.6441 & 13.4912 \\\hline \text { Number of vouchers } & 0.4618 & 0.1001 & 4.6117 & 0.0017 & 0.2309 & 0.6927 \\\hline\end{array}$ Test the significance of the slope against a suitable alternative, at the 5% level of significance. Justify your choice of the direction in your alternative hypothesis.