# this final exam | Mathematics homework help

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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

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.

_______________________________________________________________________________________

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.)

______________________________________________________________________________________

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.)

______________________________________________________________________________________

Q-2c.  Interpret the meaning of the Y-intercept, b0, and the slope, b1, in this problem. (5 pts.)

______________________________________________________________________________________

Q-2d.  Compute the coefficient of determination r2, and interpret its meaning.  (5 pts.)

______________________________________________________________________________________

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

_____________________________________________________________________________________________________________

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

_____________________________________________________________________________________________________________

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.)

_____________________________________________________________________________________________________________

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.)

_____________________________________________________________________________________________________________

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 customer’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.)

_______________________________________________________________________________________________________________________

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.

_____________________________________________________________

Q-6a.  State the multiple regression equation that predicts the selling price

based on the number of rooms in the neighborhood. (5 pts.)

_____________________________________________________________

Q-6b.  Interpret the regression coefficients.  (5 pts.)

_____________________________________________________________

Q-6c.  Predict the selling price for a house with 10 rooms that is located in a

quantitative partner will understand them.  (5 pts.)

_____________________________________________________________

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.)

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