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Statistics Problems

Problem 1: Corona Virus Outbreak

1.) The American Hospital Administrators Association (AHAA) reports the following information concerning the number of times senior citizens are admitted to a hospital during the Corona Virus outbreak. Forty percent are not admitted; 30 percent were admitted the first week; 20 percent the second week, and the remaining 10 percent were admitted the third week.

A survey of 200 residents of a local Senior Center, a community devoted to active seniors located in a hot bed political location, revealed 70 residents were not admitted during the outbreak, 70 were admitted to a hospital during the first week, 35 were admitted during the second week, and the remaining 25 were admitted during the third week. Your local Health expert is screaming during the news conference that 65% of the residents have been admitted and the city needs to be put on lockdown because this is almost two thirds higher than average!

Can we conclude the local senior center is consistent with the information suggested by the AHAA or is the EXPERT correct in their rhetoric? Use the .05 significance level?

2.) The gas station retail company you work for is in a price war with its competitors. None of you can compete on selection since you all sell the same product. You all keep lowering your prices on gasoline in order to drive up sales for your stores. Your boss comes in and says we should lower prices to $1.50 a gallon to really increase demand. How many sales would you expect if the price drops to this level? If this company’s gas stations can only support 1,450 customers a day, what is the lowest price that can be set in order to not drive customers away? 

Y(# of sales)=1600-(75*price) 

3.)You have come to the realization that buying a new car just makes no sense. Therefore, you have decided to buy a used car. You have done linear regression for the model of car you like and found that it follows the equation: Cost = 18,358-(1534*age). You decide that you can afford the car payments on a $15,000 car. How old must the car be for you to afford it? How old will this type of car be before it has a negative value? 

4.) (50 pts) You work as a manager for a real estate office. The agents are having trouble matching families to the types of houses they would seem to want and afford. Using your knowledge of multiple regression, you have developed a table that has tracked what families have purchased in the past year and made notes on their income (X1), family size (X2), and college education level(X3). This has corresponded to the size of home they purchase in square feet(Y). Given a family of 4, with an income level of $85,000, and a college education level of 6, calculate the square foot size of home a real estate agent should show them. What is the main driving factor for the size of home a family decides to purchase? 

Y=845+.0155(X1)+295.65(X2)-35.43(X3) 

5.) A common rumor for years is that a Cheesecake Factory is going to open a location in El Paso. Everyone knows “someone” who knows “someone” who knows they are going to open a location in El Paso. Most people in El Paso “know” a Cheesecake Factory would do well here without looking at any data. However, what most people do not realize is that Cheesecake Factory has the most restrictive requirements for opening a location. These factors include projected daily customer volume, availability of premiere locations, location to supplier’s warehouse, and availability of high-income consumers. The Cheesecake Factory looks at these factors and computes whether a store profit can be greater than $10,000,000. Given the attached data for 15 other Cheesecake Factory locations and given the values for El Paso, construct an ANOVA table and show why the Cheesecake Factory will not be opening a location in El Paso anytime soon and what is the major reason why.

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