Problem 1 - HEC



Questions of the exam are related to a study for a business-to-business situation, specifically a survey of existing customers of the company HATCO (source of data: Hair J.F. et al. Multivariate data analysis. Prentice Hall, 1998.) The data are in the file “May2001.xls”. Before using this file to answer the questions, be sure that you save on your hard disk, at least one copy of this file under another name or in another directory.

Three types of information were collected. The first type is the perception of HATCO on seven attributes identified in past studies as the most influential in the choice of suppliers. The respondents, purchasing managers of firms buying from HATCO, rated HATCO on each attribute. The second type of information relates to actual purchase outcomes, either the evaluations of each respondent’s product purchases from HATCO. The third type of information contains general characteristics of the purchasing companies (e.g., firm size, industry type).

The data provided should give HATCO a better understanding of both the characteristics of its customers and the relationships between their perceptions of HATCO and their actions toward HATCO (purchases and satisfaction). A definition of each variable and an explanation of its coding is given in the following sections.

Perceptions of HATCO

Each of the variables was measured on a graphic rating scale, where a 10-centimeter line was drawn between the endpoints, labeled "Poor" and "Excellent".

Poor Excellent

Respondents indicated their perceptions by making a mark anywhere on the line. The mark was then measured and the distance from 0 (in centimeters) was recorded. The result was a scale ranging from 0 to 10. The seven HATCO attributes rated by each respondent are as follows :

X1 Manufacturer's image – overall image of the manufacturer or supplier

X2 Product quality – perceived level of quality of a particular product (e.g., performance or yield)

X3 Overall service – overall level of service necessary for maintaining a satisfactory relationship between supplier and purchaser

X4 Delivery speed – amount of time it takes to deliver the product once an order has been confirmed

X5 Price level – perceived level of price charged by product suppliers

X6 Price flexibility – perceived willingness of HATCO representatives to negotiate price on all types of purchases

X7 Salesforce image – overall image of the manufacturer's salesforce

Purchase Outcomes

Two specific measures were obtained that reflected the outcomes of the respondent's purchase relationships with HATCO. These measures include :

X9 Usage level – how much of the firm's total product is purchased from HATCO, measured on a 100-point percentage scale, ranging from 0 to 100 percent

X10 Satisfaction level – how satisfied the purchaser is with past purchases from HATCO, measured on the same graphic rating scale as perceptions X1 to X7

Purchase Characteristics

The five characteristics of the responding firms used in the study are as follows :

X8 Size of firm – size of the firm relative to others in this market. This variable has two categories : 1 = large, 0 = small

X11 Specification buying – extent to which a particular purchaser evaluates each purchase separately (total value analysis) versus the use of specification buying, which details precisely the product characteristics desired. This variable has two categories : 1 = employs total value analysis approach, evaluating each purchase separately ; 0 = use of specification buying

X12 Structure of procurement – method of procuring or purchasing products within a particular company. This variable has two categories : 1 = centralized procurement, 0 = decentralized procurement

X13 Type of industry – industry classification in which a product purchaser belongs. This variable has two categories : 1 = industry A, 0 = other industries

X14 Type of buying situation – type of situation facing the purchaser. This variable has three categories : 1 = new task, 2 = modified rebuy, 3 = straight rebuy

The following variables in the file “May2001.xls” are the results of data management of previous columns to help you answer some of the questions of the exam.

X15 Satisfaction level (X10) for customers with centralized procurement (X12 =1)

X16 Satisfaction level (X10) for customers with decentralized procurement (X12 =0)

X17 Random numbers – you will not need that column

X18 Random numbers – you will not need that column

Problem 1. ( 10 points)

a) Obtain estimates of the mean, standard deviation, minimum and maximum of the satisfaction level with past purchases from HATCO based on the sample of 100 purchasers surveyed. (3 points)

|Mean | |

|Standard deviation | |

|Minimum | |

|Maximum | |

b) Use a 99% confidence interval to estimate the average satisfaction level of existing customers of the company HATCO and briefly give the interpretation of this interval. (4 points)

c) Obtain the new lower and upper bounds of the 99% confidence interval to estimate the average satisfaction level, if the sample size is increased to 400 and assuming the that sample mean and standard deviation did not change. (3 points)

|Lower bound | |

|Upper bound | |

Problem 2. ( 15 points)

a) What are the means and standard deviations of the satisfaction level with past purchases from HATCO, for companies in the sample with centralized and decentralized procurement respectively? (2 points)

| |Centralized procurement |Decentralized procurement |

|Mean | | |

|Standard deviation | | |

HATCO management is now interested in testing if the satisfaction level is significantly different between companies with centralized and decentralized procurement.

b) Formulate precisely the hypotheses H0 and H1 that we want to test in this problem. (2 points)

c) Before doing the test on the means, you need to check if the variances are equal or unequal. What is the p-value of the two-tailed test to compare the two variances? What do you conclude at the (=5% level? (4 points)

d) What is the p-value for the test of the hypotheses formulated in b)? (4 points)

e) Comment briefly the results of your test in d). (3 points)

Problem 3. (15 points)

The cross tabulation of the size of the firm (X8) and type of buying situation (X14) gave the following results:

|Count |Type of buying situation (X14) |

|Firm size (X8) |1= new task |2= modified rebuy |3= straight rebuy |

|0 = small |10 |16 |34 |

|1 = large |24 |16 |0 |

a) HATCO management wants to test if there is a significant relationship between the size of the firm and the type of buying situation. Obtain the p-value of the test and briefly comment the results according to the context (note: use appropriate distribution of percentages to comment on the presence or absence of a relationship). (5 points)

HATCO management hypothesizes that the proportion of firms that have centralized procurement (X12 = 1) is different in large firms (X8 = 1) compared to small firms (X8 = 0).

b) What are the proportion of firms in the survey sample that have centralized procurement in large and small firms respectively? (5 points) (In EXCEL, use “Pivot Table and PivotChart Report” in the menu “Data” to get the numbers you need to compute the proportions)

c) Obtain the p-value to test your hypotheses and give your conclusion at the (=1% level. (5 points)

Problem 4. ( 20 points)

HATCO management has long been interested in more accurately predicting the level of business obtained from its customers in the attempt to provide a better basis for production controls and marketing efforts. To this end you propose that a linear regression analysis should be attempted to predict the product usage levels (dependent variable X9) of the customers based on their perceptions of HATCO’s performance (independent variables X1 to X7). In addition to finding a way to predict usage levels, the management is also interested in identifying the significant factors (independent variables) that led to increased product usage for application in differentiated marketing campaigns.

Below are scatter plots of the usage levels (X9) with all seven attributes measuring perceptions of HATCO (X1 to X7), as well as scatter plots of the seven attributes pairwise.

The Pearson correlation coefficients are as follows:

a) Which of the above perception attributes seem(s) to explain the largest amount of variability in usage level. Justify briefly your answer. (2 points)

b) Which of the above perception attributes seem(s) to explain the lowest amount of variability in usage level. Justify briefly your answer. (2 points)

c) Based on the scatter plots and the Pearson correlation coefficients, do you expect possible multicolinearity problems in building your multiple linear regression model? Justify briefly your answer. (3 points)

d) Using EXCEL and the backward elimination procedure with the criteria of (=5% (i.e. perception attributes with a p-value > 5% in the model are removed), obtain and report below the multiple linear regression equation for the “best” model to predict usage levels. Briefly comment on the adjusted R square in this context. (8 points)

e) Based on the results of your regression model, what would be your recommendations to HATCO management? (5 points)

Solution

Problem 1

a) Use Descriptive Statistics in Excel:

|Mean |6,102 |

|Standard deviation |1,3386 |

|Minimum |3,4 |

|Maximum |9,6 |

b) 6,102 ± 0,352 or (5,750; 6,454). We are 99% confident that the true mean satisfaction level of customers is in the interval (5,750; 6,454).

c)

|Lower bound |6,102 – 0,352 x 1/(4 = 5,93 |

|Upper bound |6,102 + 0,352 x 1/(4 = 6,28 |

|T test for a mean (unknown sigma) | | | | |

|X-bar |Mu0 |n |

|Mean |6,636 |5,568 |

|Standard deviation |1,3405 |1,11418 |

b)

H0 : (centralized = (decentralized vs H1 : (centralized ≠ (decentralized

c) “F-test two-sample for variances” for testing the equality of the variances:

p-value = 2 x 0,09949 > 0,05 => do not reject H0 (or accept H0) , the variances are equal.

|F-Test Two-Sample for Variances | |

| | | |

|  |X15 |X16 |

|Mean |6,636 |5,568 |

|Variance |1,797044898 |1,241404082 |

|Observations |50 |50 |

|df |49 |49 |

|F |1,447590615 | |

|P(F ................
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