The Manager of a Fast Food Restaurant Wants to Determine

question 83

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. $$\begin{array} { | c | c | } \hline \text { Number of vouchers } & \text { Sales } \\\hline 4 & 12.8 \\\hline 7 & 15.4 \\\hline 5 & 13.9 \\\hline 3 & 11.2 \\\hline 19 & 18.7 \\\hline 10 & 17.9 \\\hline 8 & 16.8 \\\hline 6 & 15.9 \\\hline 3 & 11.5 \\\hline 5 & 13.9 \\\hline\end{array}$$ 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.

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Definitions:

Motor Oil Sales

The volume or amount of motor oil sold within a specific period.

Centered Moving Averages

A method used in time series analysis to smooth out short-term fluctuations and highlight longer-term trends or cycles by averaging data points in the middle of a set time window.

Quarterly Sales

The total sales revenue generated by a company or entity within a three-month period.

Motorcycle Dealership

A business that specializes in selling motorcycles and often provides maintenance and repair services.