Business Statistics

Question A

A researcher is testing the null hypothesis that there is no relationship between two

continuous variables (customers’ satisfaction: continuous dependent variable and

service quality: continuous independent variable). From a sample of n = 16, she

determines that b1 = +4.8 and Sb1 = 1.6.

a) What is the value of tSTAT?

(4 marks)

b) What statistical decision should the researcher make? (for 95% confidence

intervals, the t value is -2.145 and +2.145).

(4 marks)

c) Construct a 95% confidence interval estimate of the population slope, ß1 (for 95%

confidence intervals, the t value is -2.145 and +2.145).

(4 marks)

Question B

The marketing manager of a large supermarket chain has the business objective of

using shelf space more efficiently. Toward that goal, he would like to use shelf space

to predict the sales of pet food. Data is collected from a random sample of 12 equalsized

stores. For those data, SSR = 20535 and SST = 30025.

a) Determine the coefficient of determination, r2

, and interpret its meaning.

(4 marks)

b) Determine the standard error of the estimate.

(4 marks)

Question C

What is Simple Linear Regression? What are the assumptions of Simple Linear

Regression?

(5 marks)
2

Question D

A group of researchers from the UK1

has attempted to address the relationship

between business strategy and firm performance, by presenting an empirical

investigation of medium and large, high technology, industrial manufacturing firms.

Business performance was measured on a continuous scale.

Business strategy consisted of five dimensions, each also measured on a continuous

scale:

? Aggressiveness

? Analysis

? Defensiveness

? Futurity

? Riskiness

After collecting a satisfactory sample, the researchers examined the correlation

between the dependent variable (business performance) and the independent variables

(Aggressiveness, Analysis, Defensiveness, Futurity and Riskiness). Their results are

shown in Table 1, produced in SPSS.

Table 1. Correlation coefficients among the dependent & independent variables

Business performance p-value

Aggressiveness -0.04 0.75

Analysis 0.34 0.04

Defensiveness 0.29 0.03

Futurity 0.21 0.03

Riskiness 0.01 0.89

a) Give the definition of correlation. What are the general assumptions of correlation?

(6 marks)

b) Discuss the results of Table 1 in terms of their statistical significance, magnitude

and direction.

(8 marks)

c) Can you conclude that an increase in aggressiveness leads to business

performance’s decrease? Please, specify your answer.

(2 marks)

d) What would be your advice to managers who want to improve the performance of

their businesses?

(4 marks)

Question E

What are the two types of Chi-square test? Please, discuss each type.

(5 marks)