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QMB 2015 You run a call center and are concerned about customer support 100% Satisfaction A+

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EXCEL TAB 1    Desc Stats

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.)

Help Desk Calls

Day# Calls

145

230

353

469

567

645

717

846

932

1033

1159

1274

1342

1435

1538

1618

1741

1863

1972

2043

2145

2244

2348

2448

2567

2672

2741

2852

2975

3040

3134

3240

3388

3463

3538

3648

3745

3850

39150

4084

4128

4237

4352

4444

4549

4670

4775

4858

4923

5062

5110

5271

5380

5470

5541

5647

5799

5838

5929

6083

6160

6254

6335

6446

6551

6658

6772

6886

6948

7048

7151

7262

7362

7485

75

150

EXCEL TAB 2 Linear Regression

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 b0 and 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.)

SalesAgeGrowthIncomeHSCollege

$ 1,695,712.6233.160.8299$ 26,748.5173.594917.8350

$ 3,403,862.0532.670.6619$ 53,063.7988.455731.9439

$ 2,710,352.9135.660.9688$ 36,090.1473.536218.6198

$ 529,215.4633.070.0821$ 32,058.0779.178020.6284

$ 663,686.6535.760.4646$ 47,843.4284.183835.2032

$ 2,546,324.3433.812.1796$ 50,180.9793.499641.7057

$ 2,787,046.2030.981.8048$ 30,710.0878.023428.0250

$ 612,696.0530.78-0.0569$ 29,141.7070.294915.0882

$ 891,822.0332.32-0.1577$ 55,980.1570.667410.9829

$ 1,124,967.9732.530.3664$ 28,730.8863.739513.2458

$ 909,500.9831.442.2256$ 31,109.2376.905919.5500

$ 2,631,166.8833.161.5158$ 55,614.1282.945220.8135

$ 882,972.6531.870.1413$ 23,038.4365.212716.9796

$ 1,078,573.1233.41-1.0400$ 34,531.7273.494432.9920

$ 844,320.1934.051.6836$ 30,350.3680.220122.3185

$ 1,849,119.0328.892.3596$ 38,964.9487.597324.5670

$ 3,860,007.3236.110.7840$ 49,392.7785.304130.8790

$ 826,573.8832.810.1164$ 25,595.6965.588417.4545

$ 604,682.8733.051.1498$ 29,622.6180.617618.6356

$ 1,903,611.6033.500.0606$ 31,586.1080.379038.3249

$ 2,356,808.3932.681.6338$ 49,674.5679.852623.7780

$ 2,788,571.9628.521.1256$ 28,878.9881.237116.9300

$ 1,634,878.2932.891.4884$ 24,287.0870.224419.1429

$ 2,371,627.3730.504.7937$ 46,711.2487.104630.8843

$ 2,627,837.9630.291.8922$ 43,449.8180.205726.5570

$ 1,868,116.3331.291.8667$ 31,694.4575.291428.3600

$ 2,236,796.8633.051.7896$ 45,459.2277.616219.2490

$ 1,318,876.2332.930.2707$ 47,047.3485.175335.4994

$ 1,868,097.8431.843.0129$ 26,433.2474.179218.6375

$ 1,695,218.5731.083.4630$ 33,396.6681.699141.1130

$ 2,700,194.4232.180.7041$ 26,179.3673.414017.8566

$ 1,156,049.7731.69-0.1569$ 33,454.6473.716126.5426

$ 643,858.4434.030.7084$ 42,271.5078.6493

29.8734

EXCEL TAB 3 CI

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 thetotal 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-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.)

 

EXCEL TAB 4 HT

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.)

 

EXCEL TAB5 2SampTH

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? Explain your findings utilizing information from the test you conduct. (5 pts.)

 

EXCEL TAB 6 MultReg

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 () and the other on the west side (). 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. Explain your findings so that your non- quantitative partner will understand them. (5 pts.)

_____________________________________________________________________

Q-6c. Predict the selling price for a house with 8 rooms that is located in a East-side neighborhood. Explain your findings so that your non- quantitative partner will understand them. (5 pts.)

_____________________________________________________________________

Q-6d. Compute and interpret the adjusted r2. Explain your findings so that your non- quantitative partner will understand them (5 pts.)

PriceRoomsNeighborhood

309.670

307.480

340.390

346.5120

298.260

337.890

324.1100

313.280

327.890

325.380

308.560

381.3130

337.4100

346.2100

342.491

323.781

329.681

343.691

360.7111

348.39

1

 

EXCEL TAB  7 DECTREE

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. Explain your findings so that your non- quantitative partner will understand them. (5 pts.)

 

 

EXCEL TAB 8  PRO

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? What is the expected value of perfect information in this problem? Explain your findings so that your non- quantitative partner will understand them. (5 pts.)

Payoff Table

    

 Good Economic ConditionsPoor Economic Conditions 

  

Decision (Purchase)50%50% 

Apartment building$80,250.00$33,850.00 

Office building$125,250.00-$1,550.00 

Warehouse$52,750.00$40,250.00 

    

   

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[Solved] QMB 2015 You run a call center and are concerned about customer support 100% Satisfaction A+

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