Otto Carnage retired from Demolition Derby $10$ years ago and entered another profession for

which he was eminently qualified $-$ valet parking lot attendant. Otto has been very successful

and now owns a large parking structure in downtown L$.$A$.$ The business only accepts cash.

Otto suspects his cashiers of 'skimming' some of the cash by recording a smaller amount on

the cash register than the customer actually paid and pocketing the difference. To prevent

trouble with the cashier's union, Otto must be able to prove 'skimming' beyond reasonable

doubt $(\mathrm{.}01$ level of significance$)$ before any accusations are made. During the past week, Otto

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Workbook in Business Statistics, Thomas Wedel

observed the amounts paid by $100$ customers from a nearby high$-$rise using binoculars. The

$100$ cars that Otto observed had an average bill of $$10$ with a standard deviation of $$5.$ There

is an automatic sensor which records the number of cars leaving the facility gate. Last week

$10,000$ cars passed through the gate and the total cash receipts reported by the attendants was

$$90,000$ for an average of $$9$ per car.

a$.$ Can Danny prove 'skimming?$\text{'}$ State the null and alternative hypotheses. Find $Z_{\text{T}\text{e}\text{s}\text{t}}$ and

$Z_{\text{T}\text{a}\text{b}\text{l}\text{e}\text{.}}.$ What is your conclusion?

b$.$ Find the p$-$value.