Question 1117419: Margaret manages a fast food restaurant and she is concerned about customers who ask for a water cup when placing an order but fill the cup with a soft drink from the beverage fountain instead of filling the cup with water. She selected a random sample of 90 customers who asked for a water cup when placing an order and found that 33 of those customers filled the cup with a soft drink from the beverage fountain.
a. Construct 95 percent confidence interval for the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain. Write a sentence interpreting the interval you found.
b. Margaret believes that each customer who asks for a water cup, but fills it with a soda costs the restaurant $0.25. Suppose that in the month of April 3,000 customers ask for a water cup when placing an order. Use the confidence interval constructed in part (a) to give an interval estimate for the cost to the restaurant for the month of June from the customers who ask for a water cup but fill the cup with a soda.
c. If she can provide strong evidence that more than 30% of the customers who ask for a water cup actually fill the cup with soda, the restaurant will move the soda machine behind the counter and not let customers “self serve” and risk alienating customers. Should they move the soda machine?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Margaret manages a fast food restaurant and she is concerned about customers who ask for a water cup when placing an order but fill the cup with a soft drink from the beverage fountain instead of filling the cup with water. She selected a random sample of 90 customers who asked for a water cup when placing an order and found that 33 of those customers filled the cup with a soft drink from the beverage fountain.
a. Construct 95 percent confidence interval for the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain. Write a sentence interpreting the interval you found.
sample proportion = p-hat = 33/90 = 0.367
Margin of Error = 1.96*sqrt[0.367*0.633/90] = 0.05
95%CI:: 0.367-0.05 < p < 0.367+0.05
95% CI: 0.317< p < 0.417
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b. Margaret believes that each customer who asks for a water cup, but fills it with a soda costs the restaurant $0.25. Suppose that in the month of April 3,000 customers ask for a water cup when placing an order. Use the confidence interval constructed in part (a) to give an interval estimate for the cost to the restaurant for the month of June from the customers who ask for a water cup but fill the cup with a soda.
Interval of cost:: 0.25*0.317*3000 < cost < 0.25*0.417*3000
Interval of cost:: $237.50 < cost < $312.75
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c. If she can provide strong evidence that more than 30% of the customers who ask for a water cup actually fill the cup with soda, the restaurant will move the soda machine behind the counter and not let customers “self serve” and risk alienating customers. Should they move the soda machine?
She has 95% certainty that the percentage is between 31% and 41%
She should move the machine.
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Cheers,
Stan H.
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