Cases for Research Methodology

Post Graduate Diploma in Management Business Research Methods Cases for Business Research Methods Case: Apna Bazaar The biggest Retail Chain in the city “Apna Bazaar” has 8 outlets. There are many sections in Apna Bazaar but the case deals with only two sections: Toys and Grocery. Problem of Toy Section The toy section of Apna Bazaar sells 35 different varieties of toys. They have selected toys in such a manner that the selling price ranges between Rs. 145 and Rs. 180. The manager of the toy section has come up with a proposal. She wants to have one selling price for all toys. She wants to promote the toy section as “One price for any toy”. If the price is fixed at Rs. 145 the Apna Bazaar will lose out and if it is fixed at Rs. 180 the customer demand may decline drastically. Customer may buy similar toys from some other shop. Further, some customers buy only one toy while many other customers buy more than one toy at a time. The manger of the toy section randomly selected following ten orders from the sales data of past two months:

Sr. No. 1 2 3 4 5 6 7 8 9 10

Number of toys purchased 2 1 5 8 4 2 1 9 5 3

Total Bill Amount (Rs.) 312 160 850 1256 596 310 170 1368 835 534

The manger wishes to fix one selling price for all toys such that 95% of existing customers find it attractive and keep on patronizing the retail chain. Help her to decide the selling price. Problem of Grocery Section The Grocery section is facing too many customer complaints. Consumers are complaining that the weights of items such as pulses, salt, rice varieties & spices sold in polythene packs are less. Situation is getting out of control. There are cases pending in consumer court. Apna Bazaar wants to constitute a high level committee to advise them a course of action to identify the problem and solve. Detailed analyses revealed that majority of complaints were involving goods sold in two sizes of polythene packing: 200 gms and 1 kg. The chain sells eight different items in 200 gms poly packs and 6 different items in 1 kg poly packs.

Business Research Methods Cases

1

Dr. A. K. Dey

Further it was found that grocery chain uses electronic weighing machines with accuracy of 0.01 gms for filling up packets of one Kg and more. However, for less than a Kg packs, weighing machines with higher accuracy 0.005 gms are used. Based on the balances being used, Apna Bazaar claims that they are at least delivering 0.99 kg for 1kg pack and 0.195 kg for 0.2 kg pack. They are NOT cheating consumers. A proper study was carried out. Apna Bazaar wants to find out if the problem exists at all the outlets or confined to a few outlets. At one outlet for 200 gms packs 40 samples were randomly drawn and the mean weight was found to be 196 gms. The sample standard deviation was calculated to be 6 gms. 1. Formulate the hypotheses. 2. Suggest a sampling method. 3. Determine the sample size if the retail chain wish to contain error to less than 0.5 gms. 4. At 0.05 level of significance what is your conclusion? Case: Milk Powder

Store No.

Packet Colour

Actual sales (Kg)

Store No.

Packet Colour

Actual sales (Kg)

Store No.

Packet Colour

Actual sales (Kg)

The marketing manager thinks that the sale of milk powder brand “Bonnie Child” will be affected by the colours of the packets. He wishes to test three colours – White, Blue and Green. He has selected twenty-one almost identical stores and introduced each colour in seven stores. After a month he has collected the actual sales data from each store and compiled the following table:

1. 2. 3. 4. 5. 6. 7.

White Blue Green White Blue Green White

10 8 5 9 8 7 10

8. 9. 10. 11. 12. 13. 14.

Blue Green White Blue Green White Blue

7 6 8 9 4 9 6

15. 16. 17. 18. 19. 20. 21.

Green White Blue Green White Blue Green

5 8 4 2 9 5 3

(a) Help the marketing manager to determine if there is any effect of the colour of the pack on the actual sales at the significance levels of 0.10? (b) What will be your recommendation? Case: Comparing different methods of manufacturing: Three different assembly methods (let us call them as Method A, Method B and Method C) have been proposed for a new product. For prototype development Method A has been used. Rakesh has been assigned the task to test the efficiency of the three methods. To cut down the time taken to conduct the experiment, a completely randomized experimental design was chosen to determine which assembly method results in the greatest number of parts produced per hour. Randomly 18 workers were assigned to use one of the proposed methods. The numbers of units produced by each worker in one shift were noted and One Factor ANOVA used for analysis resulting into the following table: Anova: Single Factor SUMMARY Groups

Business Research Methods Cases

Count

Sum

Average

2

Varianc

Dr. A. K. Dey

Method A

6

454

Method B

6

559

Method C

6

551

ANOVA Source of Variation

SS 1138.77 8

Between Groups Within Groups Total

df 2

2521

15

3659.77 8

17

75.6666 7 93.1666 7 91.8333 3

MS 569.388 9 168.066 7

e 52.2666 7 157.366 7 294.566 7

F 3.38787 5

P-value 0.06107 8

F crit 3.68232

Rakesh was very happy to find that there is no significant difference in out puts of the three methods as now he need not change over from the method that have been used to produce the prototypes. Workers have developed some familiarity with the method and they need not be re-trained on a new method. But his manager was not convinced of the result. He felt that Rakesh has not taken into account the fact that workers’ out put may depend on their individual experience. He suggested that Rakesh selects only three workers having different experience and repeats the experiment by collecting data of two randomly chosen shifts for each worker using each of the three methods. Rakesh repeated the experiment incorporating the suggestions and produced the following table:

Worker1 Worker1 Worker2 Worker2 Worker3 Worker3

Method A 72 75 85 84 68 70

Method B 93 100 100 108 85 73

Method C 87 82 112 114 84 72

Rakesh needs your help in formulating hypotheses in the above case and drawing inferences so that he can present findings to his boss. Use α = 0.05. Case: Comparing performance of three designs of battery A manufacturer of batteries for electronic toys and calculators is considering three new battery designs. The manufacturer assigned this task to a PGDM student who approached him for summer project. The student decided to determine whether the mean lifetime in hours is the same for each of the three designs. She selected three different toys (Toy A, Toy B and Toy C) and three different calculators (Cal D, Cal E and Cal F) for testing the battery lives. With the help of a completely randomized design of experiment she produced the following ANOVA table and concluded that all the three designs of battery last for almost the same duration. (Use α = 0.05).

Business Research Methods Cases

3

Dr. A. K. Dey

Anova: Single Factor SUMMARY Groups

Count

Sum

Design A Design B

6 6

682 705

Design C

6

676

ANOVA Source of Variation

Within Groups

SS 78.1111 1 1084.16 7

Total

1162.27 8

Between Groups

df 2 15

Average 113.666 7 117.5 112.666 7

MS 39.0555 6 72.2777 8

Varianc e 41.0666 7 88.3 87.4666 7

F 0.54035 4

P-value 0.59346 6

F crit 3.68232

17

The manufacturer immediately detected a major flaw in the experimental design. He asked why she has not considered that there could be difference in power consumption between different toys and calculators. He asked her to repeat the experiment. The student repeated the experiment and reproduced following table:

Toy 1 Toy 1 Toy 2 Toy 2 Toy 3 Toy 3

Design A 104 109 112 119 120 118

Design B 106 110 117 115 130 127

Design C 104 101 114 111 121 125

She needs your help in formulating hypotheses in the above case and drawing inferences so that she can present findings to the manufacturer. Use α = 0.05.

Experimental Designs Which of the following questions can be tested experimentally and which can not? Where an experiment is possible, briefly suggest an approach. Where an experiment is not possible, explain why and suggest an alternative course of action. (a) Are Maruti Wagon R and Hyundai Santro selling in equal proportion in Delhi area? (b) If the price of a soft drink brand is dropped by 2% will the sales go up by 5%? (c) How can the performance of three major international courier companies be judged?

Business Research Methods Cases

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Dr. A. K. Dey

(d) As a recruiter how much weight age should be assigned to the four factors viz., Consistent first class academic record, CGPA at PGDM course, Work Experience and Communication skill? (e) How to find out whether PGDM pass outs are satisfied with their achievements in their professional career after ten years of passing out? (f) A large petroleum company facing a dilemma whether to change their transport vendors or not. (g) The manufacturer wishes to keep the percentage of defects to less than 2% in any batch of production. How to decide which batch to reject? (h) In an office employing 2500 workers, what is the percentage of people coming late? (i) Who buys our microwave ovens? (j) Among middle class families in Delhi and Agra is there a difference in average monthly expenditure incurred on regular food items? Case: Effectiveness of Pain Killer An experiment was conducted to study the duration of relief provided by three painkillers after a particular surgery. However, the painkillers’ effectiveness may differ for men and women due to hormonal differences. The results of the experiment carried out for the men and women are given below (all in hours): Users

Men

Women

Painkiller - I 2.5 3.5 3 3 4.5 3 4.5 2.5

Duration of relief in hours Painkiller - II Painkiller - III 6 4.5 5.5 5 5 5.5 5 4 7 6.5 6.5 6 6.5 6 4.5 5

Is there enough evidence to conclude that the painkillers provide same average relief? Is there significant difference between men and women for getting relief from the painkillers? SUMMARY

Painkiller - I

Painkiller - II

Painkiller - III

Total

Men Count Sum Average Variance

4.0000 12.0000 3.0000 0.1667

4.0000 21.5000 5.3750 0.2292

4.0000 19.0000 4.7500 0.4167

12.0000 52.5000 4.3750 1.3239

4.0000 14.5000 3.6250 1.0625

4.0000 24.5000 6.1250 1.2292

4.0000 23.5000 5.8750 0.3958

12.0000 62.5000 5.2083 2.1117

8.0000

8.0000

8.0000

Women Count Sum Average Variance Total Count

Business Research Methods Cases

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Dr. A. K. Dey

Sum Average Variance

26.5000 3.3125 0.6384

ANOVA Source of Variation Sample Columns Interaction Within

SS 4.1667 27.0208 0.2708 10.5000

df 1.0000 2.0000 2.0000 18.0000

Total

41.9583

23.0000

MS 4.1667 13.5104 0.1354 0.5833

46.0000 5.7500 0.7857

F 7.1429 23.1607 0.2321

42.5000 5.3125 0.7098

P-value 0.0155 0.0000 0.7952

F crit 4.4139 3.5546 3.5546

Case: Change of Air fares Airline companies change their airfares several times in a week depending on many extraneous factors that range from customer demand to change in oil price. The following table gives the air fares in thousands between two cities obtained from three different airlines for traveling on 31 Dec 2005. The fares were observed at random time points within one week prior to departure: Airline I 273 374 219 699 413 303

Airline II 471 573 293 199 819 771

Airline III 593 297 399 379 409 399

Define the population and the variable under study. Are the airfares for the three airlines more or less same? Use significance level of 0.05 and verify all the assumptions

Case: Colour of the dress Marketing Manager of MyToys.com wishes to find out if colours used for the dress of a toy bride – Orange, Red, Yellow and Green – influence the purchase decision of a girl child. In her opinion colours do influence. The sales manager of MyToys.com wishes to test if the four stores viz., White Horse, Electra, Lagoon and Blue Moon that have almost equal characteristics (location, size, number of variety carried, price charged etc.) and giving almost similar sales for past few years are really similar or they are different. The Sales Manager also wishes to test with data and prove marketing manager wrong who thinks that there is hardly any variation in the weekly sales of an item such as toy bride.

Business Research Methods Cases

6

Dr. A. K. Dey

The above four stores were selected for trial sales of the toy bride for three months. In each store every week only one dress for the bride was sold. The schedule is displayed below:

Stores Weeks First Week Second Week Third Week Fourth Week

White Horse

Electra

Lagoon

Blue Moon

Orange Green Yellow Red

Red Orange Green Yellow

Yellow Red Orange Green

Green Yellow Red Orange

At the end of the three month period sales data were collated and average weekly sales in number of units are displayed below:

Stores Weeks First Week Second Week Third Week Fourth Week

White Horse

Electra

Lagoon

Blue Moon

21 30 72 43

40 32 32 58

60 49 28 20

20 68 51 25

A two factor ANOVA has been carried out and the results are given below (some of the values are missing): Anova: Two-Factor Without Replication SUMMARY Week 1 Week 2 Week 3 Week 4

Count 4 4 4 4

Sum 141 179 183 146

Average 35.25 44.75 45.75 36.50

Variance 356.92 312.92 406.92 303.00

4 4 4 4

166 162 157 164

41.50 40.50 39.25 41.00

495.00 150.33 340.92 508.67

ANOVA Source of Variation Weeks Stores Error

SS 356.6875 11.1875 ---------

df -------------

MS -------------------

F -------------

Total

4495.938

-----

White Horse Electra Lagoon Blue Moon

P-value 0.853002 0.998916

F crit 3.862548 3.862548

The person who was given the responsibility of compiling and analyzing data, has mixed up the suitable headings and gave following three tables (if you like, you may use the information given in the tables): Table A. Table A

Table C 21

40

Business Research Methods Cases

60

20

7

Dr. A. K. Dey

Count SUM Variance Table C

Count SUM Variance Table B

Count SUM Variance

32 28 25 4 106 21.67

49 51 43 4 183 26.25

68 72 58 4 258 43.67

30 32 20 4 102 41.00

21 30 72 43 4 166 495.0 0

40 32 32 58 4 162 150.3 3

60 49 28 20 4 157 340.9 2

20 68 51 25 4 164

21 40 60 20 4 141 356.9 2

30 32 49 68 4 179 312.9 2

508.67

72 32 28 51 4 183 406.9 2

43 58 20 25 4 146 303.00

Based on the above information and assuming significance level to be 0.05: (a) Formulate hypotheses (b) Draw inferences to solve the dilemmas of the Marketing and Sales Managers. Given: F critical (3, 12, 0.05) is 3.49 Case: Selling skills & Sales Management A management institute offers PG Diploma in Business Management (PGDBM) and PG Diploma in Insurance Management (PGDIM). There are two sections in each discipline, each section having 60 students. In both the courses ‘Selling Skills & Sales Management’ is taught in the second year. The local authorities are organizing a four day exhibition cum sale of mutual funds; personal insurance products; Books, Magazines & Educational CDs and Professional courses. Accordingly they have divided the area in four pavilions and allotted stalls. In order to attract crowd on every day the organizers have scheduled different events on each day. They are on day one Opening Ceremony by film stars; on day two free show of two latest movies; on day three, being Sunday, a magic show is scheduled and on the last day the crowd pulling strategy is last two hours of discount shopping. The institute in collaboration with the organizers of the exhibition wishes to test the following: (a) Knowledge of insurance discipline will help in selling insurance products better (b) Students who have been taught Selling Skills & Sales Management will perform better in achieving sales (c) Among the visitors the propensity to buy any of the four categories of products is same (d) Different schemes to attract visitors to the exhibition do not have substantial effect

Business Research Methods Cases

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Dr. A. K. Dey

Students were selected on some random basis (draw of lots or Random number table). Finally 20 students each from PGDBM first and second year were selected. Similarly 20 students each from PGDIM first and second year course were selected. Groups were made as follows: Class

First Year Sections A & B combined 20 Students (Four groups A1, A2, A3 & A4) 20 Students (Four groups C1, C2, C3 & C4)

PGDBM PGDIM

Second Year Sections A & B combined 20 Students (Four groups B1, B2, B3 & B4) 20 Students (Four groups D1, D2, D3 & D4)

These groups of students were assigned to four pavilions on four days of the exhibition as follows (Latin Square designs): Pavilion Mutual Funds Insurance Products Books etc. Professional Courses

Day 1 A1 D4 C2 B3

Day 2 B1 A2 D2 C1

Day 3 C3 B2 A3 D1

Day 4 D3 C4 B4 A4

The average sales per student were calculated and reproduced below: Pavilion Mutual Funds Insurance Products Books etc. Professional Courses

Day 1 21 37 22 33

Day 2 32 19 35 18

Day 3 24 29 23 28

Day 4 31 28 36 23

A two factor ANOVA has been carried out and the results are given below (some of the values are missing): Anova: Two-Factor Without Replication SUMMARY Mutual Funds Insurance Products Books etc. Professional Courses

Count 4 4 4 4

Sum 108 113 116 102

Average 27 28.25 29 25.5

Variance 28.6667 54.25 56.6667 41.6667

Day 1 Day 2 Day 3 Day 4 ANOVA Source of Variation Between Products Between Days Error

4 4 4 4

113 104 104 118

28.25 26 26 29.5

63.5833 76.6667 8.66667 29.6667

SS 28.1875 36.1875

df

MS

F

Total

Business Research Methods Cases

P-value 0.91621 0.8843

F crit 3.86255 3.86255

571.938

9

Dr. A. K. Dey

The person who was given the responsibility of compiling and analyzing data, has mixed up the suitable headings and gave following three tables (if you like, you may use the information given in the tables):

Table A Table A

Table B 21

32

19

29

23

33

23

36

18

28

22

35

24

31

28

37

Count

8

8

Average

22.25

32.625

SUM

178

261

Variance

9.64

10.55

21

22

32

35

24

23

31

36

37

33

19

18

29

28

28

23

Count

8

8

Average

27.625

27.25

SUM

221

218

Variance

35.98

45.64

Table B

Business Research Methods Cases

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Dr. A. K. Dey

Table C 21

24

37

29

22

23

33

28

32

31

19

28

35

36

18

23

Count

8

8

Average

27.125

27.75

SUM

217

222

Variance

61.55

19.93

Based on the above information and assuming significance level to be 0.05: (a) Formulate hypotheses (b) Draw inferences to solve the problem. Given: F critical (1, 14, 0.05) is 4.6 Case: Workstation Designs - I A continuous production plant of chemicals is considering changing the design of the workstation at the main control room to increase the productivity of staff. The management feels that the existing workstation is not ergonomically designed and it can be substantially improved. Three vendors have offered their models: Magnum, Classic and Exotica. The vendor offering Classic is charging more than the other two brands. He claims that the tests have shown that the average time taken by workers, when 6 workers were randomly allocated to each machine, is less on his model.

Worker 1 Worker 2 Worker 3 Worker 4 Worker 5 Worker 6

Magnum 59 56 60 52 54 58

Count Mean Std Dev

6 56.50 3.08

Workstation Designs Classic Worker 7 58 Worker 8 55 Worker 9 54 Worker 10 54 Worker 11 50 Worker 12 52

Worker 13 Worker 14 Worker 15 Worker 16 Worker 17 Worker 18

6 53.83 2.71

Exotica 63 60 58 60 57 60 6 59.67 2.07

If above data set is analysed with One Way ANOVA, following table is obtained:

ANOVA Source of Variation

SS

df

MS

F

F crit

Between Groups Within Groups

102.33 105.66

Total

3.68

208

Management feels that the way test has been conducted is wrong. The test was repeated by noting the time taken by the same worker for the same job when performed on three different models.

Worker 1 Worker 2 Worker 3 Worker 4 Worker 5 Worker 6 Count Mean Std Dev

Workstation Designs Magnum Classic 55 55 56 55 58 54 52 54 54 50 51 52 6 54.33 2.58

6 53.33 1.97

Exotica 54 57 53 57 54 53

Mean 54.67 56.00 55.00 54.33 52.67 52.00

Std Dev 0.58 1.00 2.65 2.52 2.31 1.00

6 54.67 1.86

(a) Help management analyze this data and draw conclusion. (b) Is the vendor justified to charge higher price for Classic? Explain why? Case: Soft Drink A manufacturer of soft drink sells three flavours (Fresh Lime, Mango and Pineapple) in 5 liter bottles. There are three sizes of retail outlets based on sales turnovers: Large, Medium and Small. For pricing the 5 ltr bottle the manufacturer has three choices: Rs. 179 (exactly as the price of a competing brand), Rs. 149 (below the competing brand) and Rs. 199 (above the competing brand). Initially he collected replicated data of different stores for different price levels (Table 1). Next he proceeded to collect data to measure the effect of flavours as shown in Table 2. The actual data collected as per the design of Table 2 is displayed in Table 3. The two way ANOVA table as applied to Table 1 is also displayed below.

Table 1

Weekly sales units of 5 ltrs bottles Store Size by sales turnover Price 199 179 149

Large

Medium

Small

15 17 13 16 12 13

13 13 11 13 10 12

9 11 6 6 5 7

Table 2

Table 3 Weekly sales units of 5 liters bottles Store Size by sales turnover

Weekly sales units of 5 liters bottles Store Size by sales turnover Price 199 179 149

Large

Medium

Small

Fresh Lime Fresh Lime Pineapple Pineapple Mango Mango

Mango Mango Fresh Lime Fresh Lime Pineapple Pineapple

Pineapple Pineapple Mango Mango Fresh Lime Fresh Lime

Price 199 179 149

Large

Medium

Small

17 16 20 19 15 17

15 14 13 13 14 11

13 13 12 10 10 10

Two way ANOVA Table as applied to Table 1 data Source of Variation Sample Columns Interaction Within Total

SS

Df

12.33

2

112

2

15.67

4

10

9

150

17

He wishes to test the effect of price levels on the sales achieved through different stores. He also wonders if there is any effect of flavours on sales. Answer following questions: a) Is the manufacturer justified in using a Latin Square Design? Why? b) Formulate hypotheses and infer your decisions. Case: Workstation Design - II A firm is on the verge of deciding to buy workstations. There are three offers from three different vendors. Each of them claims that the design submitted is the best in terms of productivity. A student of MBA has been assigned the task of testing the productivity of workers when they are made to work on these three differently designed workstations – Classic, Neo-Classic and Trendy. Five workers are selected in such a way that as per past records

their productivity, experience, average incentive earned, etc are almost similar. All workers are females and of almost same age. The student enthusiastically designed the experiment and collected data and analyzed. She made each of the five workers perform on each workstation and collected output for one hour each. The data collected and the ANOVA table is shown below: Classic 53 Worker 1 50 Worker 5 50 Worker 2 56 Worker 3 53 Worker 4 ANOVA Source of Variation Between Groups Within Groups

Total

SS 74.1333 3

df 2

119.6

12

193.733 3

14

Neo-Classic 59 Worker 2 47 Worker 3 52 Worker 5 55 Worker 1 55 Worker 4

MS 37.0666 7 9.96666 7

F 3.71906 4

Trendy 55 Worker 4 59 Worker 1 60 Worker 2 57 Worker 5 57 Worker 3

P-value 0.05535 6

F crit 3.88529 4

She recommended that there is no significant effect of the designs on the productivity and hence the firm can go in for any of the three designs based on the lowest cost. The supervisor was not happy. After going through the report he observed that experimental design employed to collect data is right, but the method used to analyze is wrong! Analyze the data with the right method and draw your conclusion.

Case: Soil Quality To study the effect of soil type on the growth of a new hybrid plant, saplings were planted on three types of soil (clay, sand, loam) and the subsequent growth classified into three categories (poor, average, good). Use the output below to answer the following questions. Note some of the information has been purposely deleted from the output.

Poor Average

Chi Square Test Soil Quality Data Clay Sand Loam Observed 16 11 14 Expected 13.95 14.17 12.88 Observed 25 17 21

Total 41 63

Good

Expected Observed Expected

Total

21.44 24 29.61 65

------38 30.06 66

19.79 25 27.33 60

87 191

Chi Square = 0.300 + 0.708 + 0.097 + 0.591 + 1.045 + 0.074 + _____+ 2.096 + 0.199 = 6.172 Degrees of Freedom = _________ p – Value = 0.187 (a) State the appropriate Null and Alternative hypotheses. (b) Find the expected count for the AVERAGE–SAND cell. (Only for this cell, NOT the whole table.) (c) Find the contribution to the χ2 statistic for the GOOD–CLAY cell. (Only for this cell, NOT the whole table.) (d) How many degrees of freedom does the chi–square distribution have for the χ2 statistic for this table? (e) What is the value of the χ2 statistic for this table? (f) What is the p–value associated with the χ2 statistic for this table? (g) State your decision regarding H 0 at the α = .01 level. (h) State your practical conclusion in terms of the problem. Case: Hotel Satisfaction. An important measure of satisfaction with a hotel is the customer’s response to the question “If you return to the area for the same purpose as this trip, are you very likely to choose this hotel again?” In an effort by management to compare customer satisfaction at five resort hotels that are associated with a hotel chain on a certain tropical island, guest satisfaction cards were obtained for a one–month period from each of the five resorts. The results were analyzed and the output appears below. Note some information has been purposely deleted.

Hotel

A

B

C

D

E

Satisfaction Yes

No

Total

Observed

128

89

217

Expected

138.60

78.40

Observed

199

33

Expected

148.18

83.82

Observed

186

68

Expected

162.24

91.76

Observed

137

106

Expected

-----

-----

Observed

89

122

Expected

134.77

76.23

232

254

243

211

Total

739

418

1157

Chi – Squared = 0.811 + 1.434 + 17.427 + 30.809 + 3.481 + 6.155 + ______+ 3.777 + 15.544 + 27.481 = 109.055 Degrees of freedom = ________ p – value = 0.000 (i) State the corresponding Null and Alternative hypotheses. (j) Find the contribution to the χ2 statistic for the “Hotel D – YES” cell. (Only for this cell, NOT the whole table.) (k) How many degrees of freedom does the chi–square distribution have for the χ2 statistic in this table? (l) (m) (n) (o)

What is the value of the χ2 statistic for this table? What is the p–value associated with the χ2 statistic for this table? At the α = 0.05 level state your decision (Do we reject or fail to reject H0). Suppose you are the manager of the hotel chain on this island and you have just completed the above analysis. Your two best friends from college are coming for a week’s vacation on the island. Which hotel would you recommend they stay at and why?

Case: Neuroscience Neuroscience researchers examined the impact of environment on rat development. Rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), standard (cage with other rats), enriched (cage with other rats and toys), super enriched (cage with rats and toys changes on a periodic basis). After two months, the rats were tested on a variety of learning measures (including the number of trials to learn a maze to a three perfect trial criteria), and several neurological measure (overall cortical weight, degree of dendritic branching, etc.). The data for the maze task is below. Compute the appropriate test for the data provided below.

Count Sum Average Std Dev

Impoverished

Standard

Enriched

Super Enriched

22

17

12

8

19

21

14

7

15

15

11

10

24

12

9

9

18

19

15

12

5 98 19.6 3.51

5 84 16.8 3.49

5 61 12.2 2.39

5 46 9.2 1.92

Case: Level of Knowledge A researcher is concerned about the level of knowledge possessed by university students regarding United States history. Students completed a high school senior level standardized U.S. history exam. Major for students was also recorded. Data in terms of percent correct is recorded below for 32 students. Compute the appropriate test for the data provided below.

Count Sum Average Std Dev

Education

Business/Management

Behavioral/Social Science

Fine Arts

62

72

42

80

81

49

52

57

75

63

31

87

58

68

80

64

67

39

22

28

48

79

71

29

26

40

68

62

36

15

76

45

8 453 56.63 18.93

8 425 53.13 21.34

8 442 55.25 21.82

8 452 56.50 21.61

(a) (b) (c) (d) (e) (f) (g) (h)

What is your computed answer? What would be the null hypothesis in this study? What would be the alternate hypothesis? What probability level did you choose and why? What were your degrees of freedom? Is there a significant difference between the four testing conditions? Interpret your answer. If you have made an error, would it be a Type I or a Type II error? Explain your answer.

Case: Salary Comparison According to the sixth annual survey of ad agency employees conducted by an accounting firm, ad agency employees can expect another banner year in compensation. To investigate whether there is any difference in the annual compensation for art directors, suppose that a sample of 10 art directors was selected from each of the four regions: West, South, North Central & Northeast. The base salary (Rs 1000s) for each of the individuals sampled follows:

Count

West

South

North Central

NorthEast

60.90 45.90 62.10 66.60 68.00 65.00 49.40 62.30 62.60 57.20

50.80 39.60 44.20 40.00 53.90 45.40 61.10 42.30 38.40 38.30

49.50 42.30 35.50 49.10 56.70 41.40 51.30 49.40 42.10 55.70

65.90 58.60 49.30 52.90 48.50 52.90 52.40 48.10 46.50 45.90

10.00

10.00

10.00

10.00

Average St Dev Variance

60.00 7.22 52.09

45.40 7.61 57.91

47.30 6.78 45.94

52.10 6.15 37.85

At the α =0.05 level of significance, test whether the mean base salary for art directors is the same for each of the four regions.