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Confidence Intervals - Budget Fare

I'd like assistance in solving the following problem.

A major West Coast chain of "budget fare" hotels is planning an expansion into the mid-west. The mean rate for a single room at 50 "budget fare" hotels in the tri-city area of Columbus/Dayton/Cincinnati Ohio is $110.00 with a standard deviation of $15.00.

a) Find a 99% confidence interval for the mean rate for single rooms of all "budget fare" hotels in this region.

b) Management of the hotel chain will not accept an Error Bound (also known as the Maximum
Error of the Estimate) greater than 3% of the mean (or greater than 3.30). What, then, is the
minimum sample size n that can be used for this study?

As part of their study, hotel management gathered occupancy and room rate statistics for 15
"budget fare" hotels(5 each in each of the three cities). Following is the data collected.

DAILY ROOM RATE OR PRICE / OCCUPANCY PERCENT

Daily Rate($) Y - Occupancy (%)
64 80
71 78
75 81
79 77
85 84
99 72
105 71
109 70
112 67
118 65
120 62
131 64
138 60
160 55
199 50

What is the equation of the regression line?

Based upon hard estimates for the Period and Variable Costs of operating a "budget fare" hotel in the southern Ohio area, management knows that the chain will achieve corporate financial goals and generate a minimum pretax operating profit of 11% and return on capital employed of 27% if they are able to achieve a 80% occupancy rate (single room) at a price of $55.00 per room. They are convinced that they will be able to achieve these goals in the southern Ohio region.

Do you agree? Why?

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