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A Wendy's franchise has been averaging about $5000 worth of business on a typical Saturday with a standard deviation of σ = $500. The manager is concerned that sales are slipping, after taking into account the average value of sales for four consecutive Saturdays being $4800.

a. Formulate an appropriate hypothesis test to examine at the 10% level of significance whether the manager's worries are justified.

b. What should the level of significance be to arrive at a conclusion ?

c. Based on the sample findings, estimate the true mean of Saturday sales with 90% probability.

d. If we wanted to shorten the interval of the estimation of the true mean of Saturday sales to a width of $600 in total, what should the size of our sample be to achieve it?

e. If the true mean for Saturday sales is now $4500, what is the probability of accepting the (false) null hypothesis in (a) above (the probability of not sharing the manager's concern because of lack of evidence)?

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Statistics and Probability, Statistics

Category:- Statistics and Probability
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