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. Number of toys purchased Total Bill Amount (Rs.) 1 2 312 2 1 160 3 5 850 4 8 1256 5 4 596 6 2 310 7 1 170 8 9 1368 9 5 835 10 3 534
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.
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
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:
S to re N o. P ac k et C ol ou r A ct u al s al es ( K g) S to re N o. P ac k et C ol ou r A ct u al s al es ( K g) S to re N o. P ac k et C ol ou r A ct u al s al es ( K g)
1. White 10 8. Blue 7 15. Green 5
2. Blue 8 9. Green 6 16. White 8
3. Green 5 10. White 8 17. Blue 4
4. White 9 11. Blue 9 18. Green 2
5. Blue 8 12. Green 4 19. White 9
6. Green 7 13. White 9 20. Blue 5
7. White 10 14. Blue 6 21. Green 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
e Method A 6 454 75.66667 52.26667 Method B 6 559 93.1666 7 157.366 7 Method C 6 551 91.83333 294.5667 ANOVA Source of
Variation SS df MS F P-value F crit
Between Groups 1138.778 2 569.3889 3.387875 0.061078 3.68232 Within Groups 2521 15 168.0667
Total
3659.77
8 17
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: Method A Method B Method C
Worker1 72 93 87 Worker1 75 100 82 Worker2 85 100 112 Worker2 84 108 114 Worker3 68 85 84 Worker3 70 73 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).Anova: Single Factor SUMMARY
Groups Count Sum Average Variance
Design A 6 682 113.666 7 41.0666 7 Design B 6 705 117.5 88.3 Design C 6 676 112.6667 87.46667 ANOVA Source of
Variation SS df MS F P-value F crit
Between Groups 78.1111 1 2 39.0555 6 0.54035 4 0.59346 6 3.68232 Within Groups 1084.167 15 72.27778 Total 1162.278 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:
Design A Design B Design C
Toy 1 104 106 104 Toy 1 109 110 101 Toy 2 112 117 114 Toy 2 119 115 111 Toy 3 120 130 121 Toy 3 118 127 125
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?
(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 Duration of relief in hours
Painkiller - I Painkiller - II Painkiller - III
Men 2.5 6 4.5 3.5 5.5 5 3 5 5.5 3 5 4 Women 4.5 7 6.5 3 6.5 6 4.5 6.5 6 2.5 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 4.0000 4.0000 4.0000 12.0000 Sum 12.0000 21.5000 19.0000 52.5000 Average 3.0000 5.3750 4.7500 4.3750 Variance 0.1667 0.2292 0.4167 1.3239 Women Count 4.0000 4.0000 4.0000 12.0000 Sum 14.5000 24.5000 23.5000 62.5000 Average 3.6250 6.1250 5.8750 5.2083 Variance 1.0625 1.2292 0.3958 2.1117 Total Count 8.0000 8.0000 8.0000
Sum 26.5000 46.0000 42.5000
Average 3.3125 5.7500 5.3125
Variance 0.6384 0.7857 0.7098
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 4.1667 1.0000 4.1667 7.1429 0.0155 4.4139
Columns 27.0208 2.0000 13.5104 23.1607 0.0000 3.5546
Interaction 0.2708 2.0000 0.1354 0.2321 0.7952 3.5546
Within 10.5000 18.0000 0.5833
Total 41.9583 23.0000
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 Airline II Airline III
273 471 593 374 573 297 219 293 399 699 199 379 413 819 409 303 771 399
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.
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 White Horse Electra Lagoon Blue Moon Weeks
First Week Orange Red Yellow Green
Second Week Green Orange Red Yellow
Third Week Yellow Green Orange Red
Fourth Week Red Yellow Green 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 White Horse Electra Lagoon Blue Moon Weeks
First Week 21 40 60 20
Second Week 30 32 49 68
Third Week 72 32 28 51
Fourth Week 43 58 20 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 Count Sum Average Variance
Week 1 4 141 35.25 356.92 Week 2 4 179 44.75 312.92 Week 3 4 183 45.75 406.92 Week 4 4 146 36.50 303.00 White Horse 4 166 41.50 495.00 Electra 4 162 40.50 150.33 Lagoon 4 157 39.25 340.92 Blue Moon 4 164 41.00 508.67 ANOVA
Source of Variation SS df MS F P-value F crit
Weeks 356.6875 --- --- --- 0.853002 3.862548
Stores 11.1875 --- --- --- 0.998916 3.862548
Error --- --- ---
Total 4495.938 ---
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 C
32 49 68 30 28 51 72 32 25 43 58 20 Count 4 4 4 4 SUM 106 183 258 102 Variance 21.67 26.25 43.67 41.00 Table C 21 40 60 20 30 32 49 68 72 32 28 51 43 58 20 25 Count 4 4 4 4 SUM 166 162 157 164 Variance 495.00 150.33 340.92 508.67 Table B 21 30 72 43 40 32 32 58 60 49 28 20 20 68 51 25 Count 4 4 4 4 SUM 141 179 183 146 Variance 356.9 2 312.9 2 406.9 2 303.00
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
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 Second Year
Sections A & B combined Sections A & B combined PGDBM 20 Students (Four groups A1, A2, A3 & A4) 20 Students (Four groups B1, B2, B3 & B4)
PGDIM 20 Students (Four groups C1, C2, C3 & C4) 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 Day 1 Day 2 Day 3 Day 4
Mutual Funds A1 B1 C3 D3
Insurance Products D4 A2 B2 C4
Books etc. C2 D2 A3 B4
Professional Courses B3 C1 D1 A4
The average sales per student were calculated and reproduced below:
Pavilion Day 1 Day 2 Day 3 Day 4
Mutual Funds 21 32 24 31
Insurance Products 37 19 29 28
Books etc. 22 35 23 36
Professional Courses 33 18 28 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 Count Sum Average Variance
Mutual Funds 4 108 27 28.6667 Insurance Products 4 113 28.25 54.25 Books etc. 4 116 29 56.6667 Professional Courses 4 102 25.5 41.6667 Day 1 4 113 28.25 63.5833 Day 2 4 104 26 76.6667 Day 3 4 104 26 8.66667 Day 4 4 118 29.5 29.6667 ANOVA
Source of Variation SS df MS F P-value F crit
Between Products 28.1875 0.91621 3.86255
Between Days 36.1875 0.8843 3.86255
Error
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 B
Table A 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 Table B 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 45.64Table 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.
Workstation Designs
Magnum Classic Exotica
Worker 1 59 Worker 7 58 Worker 13 63
Worker 2 56 Worker 8 55 Worker 14 60
Worker 3 60 Worker 9 54 Worker 15 58
Worker 4 52 Worker 10 54 Worker 16 60
Worker 5 54 Worker 11 50 Worker 17 57
Worker 6 58 Worker 12 52 Worker 18 60
Count 6 6 6
Mean 56.50 53.83 59.67
Std Dev 3.08 2.71 2.07
If above data set is analysed with One Way ANOVA, following table is obtained:
ANOVA
Between Groups 102.33 3.68 Within Groups 105.66
Total 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.
Workstation Designs
Magnum Classic Exotica Mean Std Dev
Worker 1 55 55 54 54.67 0.58 Worker 2 56 55 57 56.00 1.00 Worker 3 58 54 53 55.00 2.65 Worker 4 52 54 57 54.33 2.52 Worker 5 54 50 54 52.67 2.31 Worker 6 51 52 53 52.00 1.00 Count 6 6 6 Mean 54.33 53.33 54.67 Std Dev 2.58 1.97 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.
Weekly sales units of 5 ltrs bottles Store Size by sales turnover Price Large Medium Small
199 15 13 9 17 13 11 179 13 11 6 16 13 6 149 12 10 5 13 12 7 Table 2 Table 3
Weekly sales units of 5 liters bottles Weekly sales units of 5 liters bottles Store Size by sales turnover Store Size by sales turnover
Price Large Medium Small Price Large Medium Small
199 Fresh Lime Mango Pineapple 199 17 15 13
Fresh Lime Mango Pineapple 16 14 13
179 Pineapple Fresh Lime Mango 179 20 13 12
Pineapple Fresh Lime Mango 19 13 10
149 Mango Pineapple Fresh Lime 149 15 14 10
Mango Pineapple Fresh Lime 17 11 10
Two way ANOVA Table as applied to Table 1 data
Source of Variation SS Df Sample 12.33 2 Columns 112 2 Interaction 15.67 4 Within 10 9 Total 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
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 Neo-Classic Trendy 53 Worker 1 59 Worker 2 55 Worker 4 50
Worker 5 Worker 347 Worker 159 50
Worker 2 Worker 552 Worker 260 56
Worker 3 Worker 155 Worker 557 53
Worker 4 Worker 455 Worker 357 ANOVA
Source of
Variation SS df MS F P-value F crit
Between Groups 74.13333 2 37.06667 3.719064 0.055356 3.885294 Within Groups 119.6 12 9.966667
Total 193.7333 14
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.
Chi Square Test Soil Quality Data
Clay Sand Loam Total
Poor ObservedExpected 13.9516 14.1711 12.8814 41
Expected 21.44 --- 19.79 Good Observed 24 38 25 87 Expected 29.61 30.06 27.33 Total 65 66 60 191 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
χ
2 statistic for the GOOD–CLAY cell. (Only for this cell, NOT the wholetable.)
(d) How many degrees of freedom does the chi–square distribution have for the
χ
2 statistic for this table? (e) What is the value of theχ
2 statistic for this table?(f) What is the p–value associated with the
χ
2 statistic for this table? (g) State your decision regarding H at the 0α
= .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 Satisfaction Yes No Total A Observed 128 89 217 Expected 138.60 78.40 B Observed 199 33 232 Expected 148.18 83.82 C Observed 186 68 254 Expected 162.24 91.76 D Observed 137 106 243 Expected --- ---E Observed 89 122 211 Expected 134.77 76.23
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
χ
2 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
χ
2 statistic in this table? (l) What is the value of theχ
2statistic for this table?(m) What is the p–value associated with the
χ
2 statistic for this table?(n) At the
α
= 0.05 level state your decision (Do we reject or fail to reject H0).(o) 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.
Impoverished Standard Enriched EnrichedSuper
22 17 12 8 19 21 14 7 15 15 11 10 24 12 9 9 18 19 15 12 Count 5 5 5 5 Sum 98 84 61 46 Average 19.6 16.8 12.2 9.2 Std Dev 3.51 3.49 2.39 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.
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 Count 8 8 8 8 Sum 453 425 442 452 Average 56.63 53.13 55.25 56.50 Std Dev 18.93 21.34 21.82 21.61
(a) What is your computed answer?
(b) What would be the null hypothesis in this study? (c) What would be the alternate hypothesis? (d) What probability level did you choose and why? (e) What were your degrees of freedom?
(f) Is there a significant difference between the four testing conditions? (g) Interpret your answer.
(h) 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:
West South CentralNorth NorthEast
60.90 50.80 49.50 65.90 45.90 39.60 42.30 58.60 62.10 44.20 35.50 49.30 66.60 40.00 49.10 52.90 68.00 53.90 56.70 48.50 65.00 45.40 41.40 52.90 49.40 61.10 51.30 52.40 62.30 42.30 49.40 48.10 62.60 38.40 42.10 46.50 57.20 38.30 55.70 45.90 Count 10.00 10.00 10.00 10.00
Average 60.00 45.40 47.30 52.10
St Dev 7.22 7.61 6.78 6.15
Variance 52.09 57.91 45.94 37.85
At the