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The University of Western Australia The Graduate School of Management
DATA ANALYSIS AND DECISION MAKING MGMT
Practice Substitution Test
Student Name______________________________ Student No.________________
Time: 2 hours plus 10 minutes reading time Questions: This paper contains two parts:
Part A contains 20 multiple-choice questions, each worth 1 mark. Total Part A marks: 20
Part B contains 8 case studies with short answer questions. Marks are identified within each question. Total Part B marks: 80
Total marks: 100 Answer: Please attempt to answer ALL questions. Write your answers in the space provided in this booklet. Pages: This booklet contains 38 pages including this page, statistical tables and solutions (please note solutions will not be provided with the actual test ☺). Special Conditions: This is a closed-book test with only your calculators (non- programmable), statistical tables and formulae page available for assistance. Please note that if you pass this test (50% or better) you will be able to substitute another elective unit in place of the Data Analysis and Decision Making MGMT8504 unit.
GOOD LUCK EVERYONE!!!
PART A: Multiple Choice questions (20 marks). Contains 20 questions, each worth 1 mark. Please attempt to answer ALL questions.
Circle the letter that corresponds to the most correct answer beside each of the following questions.
A1. The process of using sample statistics to draw conclusions about population parameters is called a) inferential statistics. b) experimentation. c) primary sources. d) descriptive statistics. e) the scientific method.
A2. In analysing categorical data , the following graphical device is not appropriate a) Pie chart. b) Pareto diagram. c) Stem and leaf display. d) Bar chart. e) they are all appropriate.
A3. The number of Singaporeans travelling to work by car today is an example of a) discrete numerical data. b) categorical data. c) continuous numerical data. d) discrete categorical data. e) continuous categorical data.
A4. A summary measure that is computed from only a sample of the population is called a) A parameter. b) A census. c) A statistic. d) The scientific method. e) All of the above.
A5. In a right skew distribution a) The median, mean and mode are all equal. b) The median and mode are both smaller than the mean. c) The median and mode are both larger than the mean. d) The distance between Q1 and the median and Q3 and the median is equal. e) None of the above.
A11. A group of researchers were attempting to determine whether female MBA graduates have a similar mean starting salary as male MBA graduates. What assumptions were necessary to conduct this hypothesis test? a) Both populations of salaries (male and female) must have approximate normal distributions. b) The population variances are approximately equal. c) The samples were randomly and independently selected. d) All of the above. e) (a) and (b) only.
Questions A12 to A15 relate to the example below. The membership controller at the Royal Big Bucks Golf Club believes that each member, on average, plays golf for more than 12 hours per week. To test his theory, the controller took a random sample of 16 golfers and asked them how many hours a week they played golf. The data was as follows: 12, 15, 10, 22, 7, 16, 8, 18, 17, 14, 13, 14, 8, 24, 18, 16. The mean number of hours the sample of golfers play for is 14.5 with a standard deviation of 4.844.
A12. State the null and alternative hypothesis to determine if the average number of hours played on the golf course is more than 12 hours per week. a) H 0 : μ ≤ 12 hours and H 1 : μ > 12 hours b) H 0 : μ ≥ 12 hours and H 1 : μ < 12 hours c) H 0 : μ = 12 hours and H 1 : μ ≠ 12 hours d) H 0 : x ≤ 12 hours and H 1 : x > 12 hours e) H 0 : x ≥ 12 hours and H 1 : x < 12 hours
A13. To test the hypotheses the membership controller decided to construct a one- tailed hypothesis test with a 5% significance level (i.e. α = 0.05). What is the appropriate t-critical value for a sample of size 16? a) 1. b) 1. c) 1. d) 2. e) 1.
A14. To test the hypotheses the membership controller decided to construct a one- tailed hypothesis test with a 5% significance level (i.e. α = 0.05). What is the appropriate t-statistic value? a) 2. b) 2. c) 1. d) 1. e) 2.
A15. Based on a 0.05 alpha level, the membership controller‘s decision would be: a) Reject H 0 , p-value < α = 0.05 and +t-statistic > +t-critical. b) Reject H 0 , p-value > α = 0.05 and +t-statistic < +t-critical. c) Not reject H 0 , p-value < α = 0.05 and +t-statistic > +t-critical. d) Not reject H 0 , p-value > α = 0.05 and +t-statistic < +t-critical. e) Throw his hands in the air and go and practise his putting.
A16. A retail manager wants to predict sales of umbrellas (Y) (in $000s). The manager uses a combination of the following variables: daily maximum temperature (X 1 ), number of customers in the shopping centre where the store is located (X 2 ), friendliness of staff (X 3 ), and whether or not the manager is walking the shop floor (X 4 ). Which of these variables is most likely to be the strongest predictor of umbrella sales for this retail store? a) X 1 b) X 2 c) X 3 d) X 4 e) All of these variables would have little effect on sales.
Questions A17 to A18 relate to the example below. The manager of this retail stores decides to statistically analyse the relationship between sales of umbrellas (SALES) and the daily maximum temperature (MAXTEMP). The regression model is: SALES(predicted)=520 - 5MAXTEMP.* The coefficient of correlation (R) for a random sample of 20 days between maximum temperature and umbrella sales is -0..
A17. Which of the following statements is not true? a) Daily maximum temperature is a good predictor of umbrella sales. b) A positive relationship exists between maximum temperature and umbrella sales. c) The coefficient of determination (R 2 ) is 0.49. d) If the max. temperature is 22^0 C, umbrella sales are predicted to be $410. e) If the max. temperature is 15^0 C, umbrella sales are predicted to be $445.
A18. Not satisfied with just considering the effect of daily maximum temperature on umbrella sales, the manager recorded the number of customers (CUSTOMERS) visiting the store, irrespective of whether the customer purchased an umbrella. The regression model is: SALES (predicted) = 472 - 4MAXTEMP +3.5CUSTOMERS** The new coefficient of determination is 0.59. Which of the following statements is not true? a) ‘Umbrella sales’ is the dependent variable. b) Assuming the maximum temperature is kept constant, the average effect of each extra customer is to increase sales by $3.5. c) Assuming the number of customers is kept constant, the effect of a one- degree increase in maximum temperature is to increase sales by $4. d) 59% of the variation in umbrella sales is explained by the combined variation in maximum temperature and number of customers. e) Umbrella sales are negatively correlated with daily maximum temperature and positively correlated with the number of customers in the store.
PART B: Case Study Questions (80 marks). Contains 8 case studies with short answer questions. Please attempt to answer all questions.
Case Study A (6 marks). Please attempt to answer ALL questions.
The coaches of a local football team wanted to determine whether the players on their team were older than those of others teams. They recorded the ages of the players on two of the teams as follows:
Team A: 25, 25, 28, 30, 25, 25, 24, 25, 22, 21, 19, 20, 22, 33, 28, 25, 26, 30, 28, 22, 24, 21 Team B: 23, 23, 26, 27, 24, 20, 21, 23, 25, 21, 22, 29, 28, 29, 28, 27, 23, 23, 26, 32, 23, 20
A set of descriptive statistics was computed for both teams’ ages, along with adjacent five- number summaries (below) and box plots (next page).
Team A Team B Mean 24.909 Mean 24. Standard Error 0.756 Standard Error 0. Median 25 Median 23. Mode 25 Mode 23 Standard Deviation 3.544 Standard Deviation 3. Sample Variance 12.563 Sample Variance 10. Kurtosis -0.112 Kurtosis -0. Skewness XXXX Skewness XXXX Range 14 Range 12 Minimum 19 Minimum 20 Maximum 33 Maximum 32 Sum 548 Sum 543 Count 22 Count 22 Confidence Level (95.0%)
1.571 Confidence Level (95.0%)
Five-number Summary Team A Team B
Minimum (^) 19 20
First Quartile 22 23 Median 25 23. Third Quartile 28 27 Maximum 33 32
Box Plots for Age
Team A
Team B
15
20
25
30
35
Team
Ag e
- Given one of the aims of this analysis is to make inferences about the average age of all football players (there are 16 teams in the competition), what type of sampling scheme has been used here? Briefly explain. ( marks)
- For which team, Team A or Team B, is age more variable? Refer to and/or compute two different statistics to support your answer. (2 marks)
- By using either descriptive statistics or box plots, comment on the skewness of both teams’ age distributions. (2 marks)
Case Study C (9 marks). Please attempt to answer ALL questions.
The growing use of bicycles to commute to work has caused many cities to create exclusive bicycle lanes. These lanes are usually created by disallowing parking on streets that formerly allowed curb-side parking. Shop-owners on such streets complain that the removal of parking will cause their businesses to suffer. To examine this problem a mayor of a large city decided to launch an experiment on one busy street that had one-hour parking meters. The meters were removed and a bicycle lane was created. The mayor asked three businesses (a drycleaner, a doughnut shop, and a convenience store) in one block to record daily sales for two complete weeks (Sunday to Saturday) prior to the change and two complete weeks after the change, the assumption being that the removal of parking bays would result in fewer sales. The data are presented below:
Day Drycleaner Doughnut Shop Convenience Store Sales Before
Sales After
Sales Before
Sales After
Sales Before
Sales After Sunday 195 173 319 317 307 287 Monday 194 204 347 331 393 390 Tuesday 146 153 306 301 407 394 Wednesday 186 184 316 306 352 314 Thursday 178 168 324 318 337 308 Friday 146 145 339 340 445 419 Saturday 161 141 272 248 440 429 Sunday 190 185 285 284 357 320 Monday 162 157 312 284 389 354 Tuesday 154 154 346 325 410 398 Wednesday 153 163 266 268 314 270 Thursday 172 175 309 282 359 339 Friday 174 170 315 268 425 380 Saturday 141 145 258 262 310 272
- State the null hypothesis for the doughnut shop. Write the null hypothesis in words AND statistical notation. (2 marks)
- State the alternative hypothesis for the doughnut shop. Write the alternative hypothesis in words AND statistical notation. (2 marks)
Following is the EXCEL output.
t-Test: Paired Two Sample for Means-- Drycleaners t-Test: Paired Two Sample for Means- Doughnut Shop t-Test: Paired Two Sample for Means- Convenience Store
- Mean 165.5 Sales After Sales Before
- Variance 321.961538 351.
- Observations
- Pearson Correlation 0.
- Hypothesized Mean Difference
- df
- t Stat -0.
- P(T<=t) one-tail 0.
- t Critical one-tail 1.
- P(T<=t) two-tail 0.
- t Critical two-tail 2.
- Mean 295.285714 308. Sales After Sales Before
- Variance 812.065934 809.
- Observations
- Pearson Correlation 0.
- Hypothesized Mean Difference
- df
- t Stat -3.
- P(T<=t) one-tail 0.
- t Critical one-tail 1.
- P(T<=t) two-tail 0.
- t Critical two-tail 2.
- Mean 348.142857 374. Sales After Sales Before
- Variance 2941.82418 2270.
- Observations
- Pearson Correlation 0.
- Hypothesized Mean Difference
- df
- t Stat -7.
- P(T<=t) one-tail 2.8273E-
- t Critical one-tail 1.
- P(T<=t) two-tail 5.6547E-
- t Critical two-tail 2.
Case Study D (9 marks). Please attempt to answer ALL questions.
The owners of Big Bucks car yard are concerned with their declining sales over the past few months. As a result they want to determine whether there is a difference in the motivation of sales staff paid on an hourly rate plus commission or on commission only (but at a higher percentage rate). Of 24 randomly selected newly trained sales staff, 12 were paid at an hourly rate and 12 on a commission basis only. The following data represent the sales in volume (in thousands of dollars) achieved during the first month on the job.
Hourly Rate Commission
147 330
224 472
118 195
209 489
126 386
372 462
197 509
260 312
372 227
451 325
447 518
328 476
To determine whether there is any difference in the sales volume of the two motivational methods one of the owners of Big Bucks, who has a statistical background, decided to analyse the data with a hypothesis test at a 5% significance level (α). The Excel output is below.
- State the null hypothesis for this situation. Write the null hypothesis in words AND statistical notation (2 marks)
- State the alternative hypothesis for this situation. Write the alternative hypothesis in words AND statistical notation. (2 marks)
Following is the EXCEL output.
- Use this information to decide whether you should reject the null hypothesis in this case. Show all workings. (Use alpha=0.05). (1 mark)
- Draw a conclusion with respect to the problem. (2 marks)
- Describe what a Type 1 error would be for this situation. (2 marks).
t-Test: Two-Sample Assuming Equal Variances
Hourly Commission Mean 270.9166667 391. Variance 14407.90152 12557. Observations 12 12 Pooled Variance 13482. Hypothesized Mean Difference 0 Df 22 t Stat -2. P(T<=t) one-tail 0. t Critical one-tail 1. P(T<=t) two-tail 0. t Critical two-tail 2.
Case Study F (16 marks). Please attempt to answer ALL questions.
Brokenleggen is a medieval village in the Swiss Alps whose unemployment level is primarily influenced by the influx of skiers, particularly during the snow-laden months of October- March. The following data represent the number of unemployed residents of Brokenleggen during the 20 economic quarters from 1996-2000.
Quarter/Year Unemployed Quarter/Year Unemployed March 1996 105 September 1998 241 June 1996 214 December 1998 128 September 1996 226 March 1999 121 December 1996 126 June 1999 217 March 1997 112 September 1999 250 June 1997 232 December 1999 122 September 1997 224 March 2000 126 December 1997 131 June 2000 229 March 1998 106 September 2000 259 June 1998 208 December 2000 133
The chief statistician of Brokenleggen - also the mayor - wants to isolate the seasonal effects of the town’s unemployment to assist in the prediction of future unemployment levels. The data were plotted (see graph below) and the line of best fit was computed.
Unemployment in Brokenleggen
y = 1.2135x + 162. R^2 = 0. 0
Quarter (0=March 1996)
Unemployed
The regression equation shown above is Y= 162.76 + 1.2135X, where X = quarter/year (March 1996 is X=0), and Y=predicted unemployment level. The coefficient of determination (R 2 ) =0.
Further data analysis produced the following quarterly seasonal indexes: MARCH = 0. JUNE = 1. SEPTEMBER = 1. DECEMBER = 0.
The quarterly seasonal indexes were used to seasonally adjust the data. The regression equation is: 164.46 + 1.0163*(coded quarter) where March 1996 is coded 0. The R 2 is 0.3982. The data are graphically displayed below.
De-seasonalised Unemployment in Brokenleggen 1996-
y = 1.0163x + 164. R^2 = 0. 140
Quarter (0=March 1996)
Unemployed
- Comment briefly of the main reason why the line of best fit (trend line) has an extraordinarily low coefficient of determination (R^2 ) value. (2 marks)
- Interpret the June seasonal index value in relation to the seasonality of unemployment in Brokenleggen. (2 marks)
- Interpret the December seasonal index value in relation to the seasonality of unemployment in Brokenleggen. (2 marks)
Case Study G (18 marks). Please attempt to answer ALL questions.
A DADM student decides to predict the selling price for apartments in an upmarket suburb of Perth. The student randomly collected data for 31 apartments sold in the last 6 months. The variables included the age of the apartment in years (AGE) , the proximity of the apartment to transport- whether or not it was close to public transport (dummy variable 1=close, 0= not close) (TRANS) , the location of the apartment measured by the kilometres away from the centre of the city (LOCATION) , the number of bedrooms in the apartment (BEDRMS) , the number of bathrooms in the apartment (BATHRMS). The information is as follows:
Following is the correlation matrix.
Selling Price (000s) Age (yrs) Close to Transport Location No. Bedrooms No. Bathrooms Y X1 X2 X3 X4 X 640 14 0 13 1 1 570 20 0 16 1 1 890 4 1 9 5 2 670 14 0 12 2 1 750 9 0 9 3 2 680 12 0 13 2 2 460 20 0 21 1 1 770 7 1 8 4 2 650 14 0 11 2 1 620 21 0 12 1 1 890 4 1 7 5 2 560 15 0 20 1 1 670 13 0 9 2 1 680 15 0 11 2 1 640 13 0 14 2 1 760 12 1 7 3 1 850 5 1 5 5 2 790 8 1 7 4 1 880 3 1 6 5 1 920 1 1 3 6 3 740 10 0 7 2 1 570 16 0 17 1 1 680 13 0 12 3 1 670 14 0 10 2 1 930 2 1 4 6 2 560 18 0 17 1 1 520 14 0 18 1 1 510 21 0 20 1 1 710 11 0 7 2 1 740 10 0 6 3 2 670 16 0 10 2 1
Selling Price (000s) Age (yrs) Close to Transport Location No. Bedrooms No. Bathrooms Selling Price (000s) 1 Age (yrs) -0.934674404 1 Close to Transport 0.805954172 -0.790302 1 Location -0.910099748 0.804188 -0.629731296 1 No. Bedrooms 0.945762931 -0.933053 0.876556176 -0.799555 1 No. Bathrooms 0.668905203 -0.706306 0.547251139 -0.537283 0.724347265 1
- Comment briefly on the correlation matrix. Specifically in relation to the relationship between the dependent variable and each independent variable (i.e. strength and direction). (2.5 marks)
Following is the regression output.
Consider Model Cp k R Square Adj. R Square Std. Error This Model? X1 68.65023 2 0.873616 0.869258181 45.29094 No X1X2 61.52526 3 0.885673 0.877506964 43.83891 No X1X2X3 9.019199 4 0.957693 0.952991844 27.15755 No X1X2X3X4 4.008372 5 0.966956 0.961872477 24.45813 Yes X1X2X3X4X5 6 6 0.966967 0.960360651 24.93833 Yes X1X2X3X5 10.09606 (^5) 0.958912 0.952591243 27.27303 No X1X2X4 40.44016 4 0.916176 0.906861975 38.22676 No X1X2X4X5 40.59247 5 0.918617 0.906096708 38.38349 No X1X2X5 63.35223 4 0.885902 0.873224221 44.5987 No X1X3 16.86854 3 0.944679 0.940727086 30.49525 No X1X3X4 2.430656 4 0.966398 0.962664642 24.20272 Yes X1X3X4X5 4.354739 5 0.966498 0.961344409 24.62693 Yes X1X3X5 18.09873 4 0.945696 0.939661959 30.76803 No X1X4 38.9175 3 0.915545 0.909512572 37.67889 No X1X4X5 39.60948 4 0.917273 0.908081511 37.97567 No X1X5 70.53488 3 0.873769 0.864752124 46.06481 No X2 238.2197 2 0.649562 0.637478063 75.41733 No X2X3 36.96801 3 0.918121 0.912272437 37.09984 No X2X3X4 6.983359 4 0.960383 0.95598071 26.28001 No X2X3X4X5 8.940519 5 0.960439 0.954352974 26.76149 No X2X3X5 27.28539 4 0.933557 0.926174816 34.03348 No X2X4 53.13213 3 0.896763 0.889389046 41.65845 No X2X4X5 54.07219 4 0.898164 0.886848459 42.13415 No X2X5 184.1331 3 0.72367 0.703932102 68.15531 No X3 102.9606 2 0.828282 0.822360226 52.79273 No X3X4 5.168036 3 0.960139 0.957291382 25.88581 No X3X4X5 7.163328 4 0.960145 0.955716493 26.35876 No X3X5 70.51747 3 0.873792 0.864776773 46.06061 No X4 52.86948 2 0.894468 0.890828471 41.3865 No X4X5 54.45391 3 0.895017 0.887517819 42.00934 No X5 391.1949 2 0.447434 0.428380177 94.70168 No
