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SEMESTER 2 SESSION 2021/2022

BT10403

STATISTICS FOR BUSINESS AND ECONOMICS

QUESTION 1

A personal computer assembly company is interested in studying the time it takes to assemble a computer under different time periods. Specifically, two factors are to be controlled: the number of individual work stations in the line (Factor B) and whether the assembly was done on morning shift, noon shift, or night shift (Factor A). The following data were obtained in the study where the response variable is the time required (in hours) to assemble the PC from start to final test.

Carry out appropriate statistical tests using a significance level of 10%.

a. Calculate the following:

i. Sum of squares and mean square for Factor A . (3 marks)

ii. Sum of squares and mean square for Factor B. (3 marks)

iii. Sum of squares and mean square for the interaction between Factor A and B.

(4 marks)

iv. Total sum of squares. (2 marks)

v. Error sum of squares and mean square error. (4 marks)

b. Test whether the mean time to complete assembly of the PCs differs by number of individual work stations in the line.

i. State the null and alternative hypotheses. (1 mark)

ii. Compute the test statistic and its -value. (3 marks)

iii. Conclude whether the mean time to complete assembly of the PCs differs by number of individual work stations in the line. (1 mark)

c. Test whether the mean time to complete assembly of the PCs differs by work shifts.

i. State the null and alternative hypotheses. (1 mark)

ii. Compute the test statistic and its -value. (3 marks)

iii. Conclude whether the mean time to complete assembly of the PCs differs by work shifts. (1 mark)

d. Test whether there is interaction between the number of individual work stations and work shifts.

i. State the null and alternative hypotheses. (1 mark)

ii. Compute the test statistic and its -value. (3 marks)

iii. Conclude whether there is interaction between number of individual work stations and work shifts. (1 mark)

QUESTION 2

A social scientist believes that the marital status of Malaysian men is dependent on their religious affiliation. A sample of 500 Malaysian men is surveyed, and the results are tabulated as shown below:

State the competing hypotheses of this test.

Calculate the expected frequencies.

What is the value of the test statistic and its associated -value? State the conclusion at = 0.05.

QUESTION 3

A recent article in local paper listed the “Best Small and Medium Enterprise”. We are interested in the current results of the enterprises’ sales and earnings. A random sample of 12 enterprises was selected for this. The table below reported their sales and earnings (in RM Millions).

a. State the simple linear regression model where earnings is treated as the dependent variable while:

i. The sales (RM Millions) is the sole independent variable. (1 mark)

ii. The assets (RM Millions) is the sole independent variable. (1 mark)

b. Based on the ordinary least square estimate, form the simple linear regression equation by calculating the estimated slope (b1) and the intercept (b0) when:

i. The sales (RM Millions) is the sole independent variable. (4 marks)

ii. The assets (RM Millions) is the sole independent variable. (4 marks)

c. State the appropriate multiple linear regression model. (1 mark)

d. Using any statistical software, determine the multiple linear regression equation for (c) and show the output of the software. (3 marks)

e. Based on the -value produced in (d), determine whether the sales (RM Millions) and assets (RM Millions) are significant in explaining the earnings (RM Millions). Assume that the significance level is set at 10%. (2 marks)