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This final exam
This final exam is comprised of eight worksheets covering various key topics of the Harvard fully online eLearning course on Quantitative Methods.
Complete the exam as if you were submitting this workbook to a lay person not familiar with quantitative methods such that they could easily understand your arguments, graphs, mathematical evidence and conclusions.
Please show all of your work. It is not enough to simply get right answers on this Exam or to just explain the mathematical process in a text box; you must show your work to demonstrate that YOU know how to arrive at correct answers using Excel calculations, functions, and/or appropriate utility. If a utility is used, the specific utility must be pasted to the respective worksheet.
There is a deadline for the submission of this exam. You are responsible for submitting this completed workbook to your coach before the deadline. Use Lastname.Firstname.FinalExam as the file name of your document.
Q-1a. You run a call center 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 75-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. (5 pts.)
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 33 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 33 set are:
Sales ------Latest one month sales total (dollars)
Income ---Median family income of customer base (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.
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Q-2a. Construct a scatter plot, using sales as the dependent variable and median family income as the
independent variable. Discuss the scatter plot. (5 pts.)
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Q-2b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients
b0and b1 and state the regression equation. (5 pts.)
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Q-2c. Interpret the meaning of the Y-intercept, b0, and the slope, b1, in this problem. (5 pts.)
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Q-2d. Compute the coefficient of determination r2, and interpret its meaning. (5 pts.)
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Q-2e. Construct a 95% confidence interval estimate of the population slope and interpret its meaning. ( 5 pts.)
Q-3a. A sample of students from an introductory psychology class were polled regarding the number of hours they spent studying for the last exam. All students anonymously submitted the number of hours on a 3 by 5 card. There were 24 individuals in the one section of the course polled. The data was used to make inferences regarding the other students taking the course. Construct a 95% confidence interval estimate . Explain your findings so that your non-quantitave partner will understand them. Their data is below: (5 pts.)
20 18 7.5 11 10 3.5 7.5 18 19 2.5 9 14
9 14 14.5 17 22 4.5 10.5 15 5 8.5 8 20
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Q-3b. A sample of Alzheimer's patients are tested to assess the amount of time (in minutes) in stage IV sleep. It has been hypothesized that individuals sufferering from Alzheimer's Disease may spend less time per night in the deeper stages of sleep. The number of minutes spent is Stage IV sleep is recorded for thirty patients (refer to sample data below of stage IV sleep over a 24 hour period). Compute a 95 percent confidence interval for this data. What does this information tell you about a particular individual's (an Alzheimer's patient) stage IV sleep? Explain your findings so that your non-quantitative partner will understand them. (5 pts.)
Stage IV Sleep in Minutes
28.5 37.4 18.5 53.2 61.3 18.75 33.9 27.1 73.0 53.4 66.0 20.5 51.7 57.25 35.6
33.4 25.1 65.3 55.0 35.0 19.25 81.5 44.1 28.7 36.5 32.2 47.3 41.7 39.75 18.3
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Q-3c. A large retail corportation plans to sample sales receipts of its meat department to estimate the average size (in dollars) of a customer purchase. Previous analysis suggest that the standard deviation of the purchase amount is approximately $50.72. In order to calculate a 95% confidence interval of the total width less than $6.50, how many sales receipts should the corportion include in the sample? Explain your findings so that your non-quantitative partner will understand them. (5 pts.)
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Q-3d. A survey of 850 workers were asked how much they used the Internet at work. 578 said they used the internet within limits, and 255 said that they did not use the Internet within limits. Construct a 95% confidence interval estimate for the proportion of all workers who did not use the Internet within limits. Explain your findings so that your non-quantitative partner will understand them. (5 pts.)
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Q-3e. You are the designer for your company's web site. You have data to indicate that the mean download time for the homepage is 5.8 seconds and that the standard deviation of download time is 2.1 seconds. If we assume that the download times are normally distributed, what percent of users will wait between 4 and 8 seconds for the homepage to download? Explain your findings so that your non-quantitative partner will understand them. (5 pts.)
Q-4a. You are the manager of a popular retail store. You want to determine whether the population mean wait time for customer to
check-out has changed in the past month from its previous population mean value of 4.25 minutes. From past experience, you
can assume that the population is normally distributed with a population standard deviation of 1.6 minutes. You select a sample
of 43 customerâ€™s wait time to check-out during a one hour period. The sample mean is 4.75 minutes. Determine whether there
is evidence at the 0.05 level of significance that the population mean wait time to check-out has changed in the past month from
its previous population mean value of 4.25 minutes. Explain your findings utlizing information from the hypothesis test you
conduct. (5 pts.)
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Q-4b. You are the manager of a fast-food restaurant. Based on a sample of two-hundred fifty drive-through orders, you discovered that
orders were filled correctly 86.5% of the time. In an effort to improve the amount of orders filled correctly, you developed a new
process to fill orders. After sampling two-hundred fifty orders under this new process, the results reviled that 225 orders were
filled correctly. At the 0.01 level of significance, can you conclude that the new process population proportion of orders filled
correctly is higher than the proportion of orders filled under the old process? Explain your findings utilizing information from the
test you conduct. (5 pts.)
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 27 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? (5 pts.)
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.
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Q-6a. State the multiple regression equation that predicts the selling price
based on the number of rooms in the neighborhood. (5 pts.)
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Q-6b. Interpret the regression coefficients. (5 pts.)
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Q-6c. Predict the selling price for a house with 10 rooms that is located in a
East-side neighborhood. Explain your findings so that your non-
quantitative partner will understand them. (5 pts.)
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Q-6d. Compute and interpret the adjusted r2. (5 pts.)
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 $120 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 $550,000, 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 $135
million in lost earnings. Alternatively it is estimated that there is a 95% probability of only slight
losses of around $1.1 million. Using decision tree analysis, determined whether the bank should
install the new power generator. (5 pts.)
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 andwhat is the expected value of
perfect information in this problem ? Explain your findings so that your non-
quantitative partner will understand them. (5 pts.)
Solution Description