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# Graphs, Variables, Confidence Intervals, Population Mean Value, Highest EMV

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Q-1a. You run a small Internet business and are concerned about customer support service levels on the Help Desk. You want to know how many calls per day are handled by your help desk staff. You collect the data at left over a 90-day period. Use appropriate descriptive statistics to make sense of this data. Use an appropriate graph also. Explain your findings so that your non-quantitative partner will understand them.

Can demographic information be helpful in predicting sales at sporting goods stores? The data at left are monthly sales totals from a random sample of 38 stores in a large chain of nationwide sporting goods stores. All stores in the franchise, and thus within the sample, are approximately the same size and carry the same merchandise. The county, or in some cases counties, in which the store draws the majority of its customers is referred to here as the customer base. For each of the 38 stores, demographic information about the customer base is provided. The variables in the data set are:
Sales - Latest one month sales total (dollars)
Age - Median age of customer base (years)
HS - Percentage of customer base with a high school diploma
College - Percentage of customer base with a college diploma
Growth - Annual population growth rate of customer base over the past 10 years.
Income - Median family income of customer base (dollars)

Q-2a. Construct a scatter plot, using sales as the dependent variable and median family income as the independent variable. Discuss the scatter plot.

Q-2b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.

Q-2c. Interpret the meaning of the Y-intercept, b0, and the slope, b1, in this problem.

Q-2d. Compute the coefficient of determination r2, and interpret its meaning.

Q-2e. Construct a 95% confidence interval estimate of the population slope and interpret its meaning.

Q-3a. A stationery store wants to estimate the mean retail value of greeting cards purchased by its customers when they visit the store. A random sample of 15 customers indicates a mean amount of \$2.55 with a standard deviation of \$0.44 per customer per visit. Assuming a normal distribution, construct a 95% confidence interval estimate of the mean retail value of greeting cards purchased by its customers.

Q-3b. A paper manufacturer has a production process that operates continuously throughout an entire production shift. The paper is expected to have a mean length of 11 inches, and the standard deviation of the length is 0.02 inches. At periodic intervals, a sample is selected to determine whether the mean paper length is still equal to 11 inches or whether something has gone wrong in the production process to change the length of the paper produced. You select a random sample of 100 sheets, and the mean paper length is 10.998 inches. Construct a 95% confidence interval estimate for the population mean paper length.

Q-3c. A survey of 705 workers asked how much they used the Internet at work. 423 said they used it within limits, and 183 said that they did not use the Internet at work. Construct a 95% confidence interval estimate for the proportion of all workers who use the Internet within limits.

Q-3d. You are the designer for your company's web site. You have data to indicate that the mean download time for the homepage is 7 seconds and that the standard deviation of download time is 2.0 seconds. If we assume that the download times are normally distributed, what percent of users will wait between 5 and 10 seconds for the homepage to download?

Q-4a. You are the manager of a fast food restaurant. You want to determine whether the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. From past experience, you can assume that the population is normally distributed with a population standard deviation of 1.2 minutes. You select a sample of 25 orders during a one hour period. The sample mean is 5.1 minutes. Determine whether there is evidence at the 0.05 level of significance that the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes.

Q-4b. You have just opened your new fast-food restaurant. And you have developed a new process to ensure that orders at the drive-through are filled correctly. The previous process filled orders correctly 85% of the time. Based on a sample of a hundred orders using the new process, 94 were filled correctly. At the 0.01 level of significance, can you conclude that the new process has increased the proportion of orders filled correctly?

Q-5a. One of the important features of a camera is the battery life as measured by the number of shots taken until the battery needs to be recharged. The data at left contain the battery life of 31 subcompact cameras and 15 compact cameras. Assuming that the population variances from both types of digital cameras are equal, is there evidence of a difference in the mean battery life between the two types of digital cameras at the 95% confidence level?

A real estate Association in a suburban community would like to study the relationship between the size of a single-family house (as measured by number of rooms) and the selling price of the house (in thousands of dollars). Two different neighborhoods are included in the study, one on the east side of the community (=0) and the other on the west side (=1). A random sample of 20 houses was selected with the results given at left.

Q-6a. State the multiple regression equation that predicts the selling price based on the number of rooms in the neighborhood.

Q-6b. Interpret the regression coefficients.

Q-6c. Predict the selling price for a house with nine rooms that is located in an East-side neighborhood.

Q-6d. Compute and interpret the adjusted r2.

Q-7a. The management of a bank in the Caribbean was concerned about the potential loss that might occur in the event of a hurricane. The bank estimated that the loss from one of these storms could be as much as \$100 million including losses due to interrupted service and customer relations. One project the bank is considering is the installation of an emergency power generator at its operations headquarters. The cost of the emergency generator is \$800,000, and if it is installed no losses from this type of storm will be incurred. However, if the generator is not installed, there is a 10% chance that a power outage will occur during the next year. If there is an outage there is a 5% probability that the resulting losses will be very large or approximately \$80 million in lost earnings. Alternatively, it is estimated that there is a 95% probability of only slight losses of around \$1 million. Using decision tree analysis, determined whether the bank should install the new power generator.

An investor is to purchase one of three types of real estate. The investor must decide among an apartment building, an office building, and a warehouse. The future states of nature that will determine how much profit the investor will make are good economic conditions and poor economic conditions. The profits that will result from each decision in the event of each state of nature are shown above.

Q-8a: Which investment has the highest EMV?

Q-8b: What is the expected value of perfect information in this problem ?