Question 1 (16 Marks)
A psychologist was interested in determining which factors affected how happy workers are in
their jobs. She collected information from a number of her clients who were employed in the
mining industry. Each subject was presented with ten positive statements relating to their job
and asked to rate them on a scale of 1 â€’ 10 as to how positive they felt about the statement.
The scores were then totalled to provide an overall rating of satisfaction. This variable
‘Satisfaction’ is the outcome variable. Note that we shall treat all the variables as numerical.
There is a two page limit on this question.
Use the MINITAB worksheet happyworkers.mtw to answer the following questions.
Variable Name Variable Description
Supervisor A measure of relationship with their supervisor on a scale of 1 â€’ 5
Environment A measure of the quality of the work environment on a scale of 1 â€’ 10
Hours Number of hours worked per week
Opportunities A measure of how the employee rates their opportunities for
advancement on a scale of 1 â€’ 5
Satisfaction A total rating of satisfaction on a scale of 1 â€’ 100
Source: Black, K. et al, “Australasian Business Statistics”. Wiley 2013 (adjusted).
a. Provide a scatter plot matrix (matrix plot) showing the relationship between each of
the variables described above and use this to answer the following:
i. What approximately is the satisfaction rating of the employee with the highest
ii. Does the employee with the highest satisfaction rating have the highest measure
on each of the prospective predictors?
iii. If your answer to part ii. was ‘No’ indicate which predictor/s do not have the
highest measurement for the employee with the highest satisfaction rating?
b. Provide a correlation matrix and use it to answer the following:
i. Which predictor has the weakest relation with satisfaction rating?
ii. Which predictor is most strongly related to satisfaction rating?
iii. Which predictors from those described above are significantly related to
satisfaction rating at a 5% significance level?
iv. Which predictors are significantly related to each other?
v. Calculate the coefficient of determination for the relation between satisfaction
rating and the number of hours worked by employees.
c. Carry out a global test to determine whether any of the potential determinants listed
above are useful for predicting the satisfaction rating of employees. Use a 5%
significance level to conduct this test. Do not comment on test assumptions here.
d. Using a 5% significance level and a model reduction process to identify the best model
for predicting satisfaction rating. Write out your final model.
e. Interpret the coefficient of one of the variables in the final model you selected above.
f. Comment on the model assumptions for your final model.
g. Use the model you chose above to predict, if possible, the satisfaction rating for an
employee who works 40 hours per week and who gives a measure of 3 on each of the
relationship with his supervisor, the quality of the work environment and the rating on
his opportunity for advancement.
Question 2 (16 marks)
A study was conducted by a large engineering company to compare the numbers of hours
worked by various sections of its administrative staff. 100 administrative employees of the
company were surveyed and the number of hours each had worked during the previous week
was recorded. The employees surveyed were employed as receptionists, secretaries, mail
clerks, typists and payroll clerks. The data can be found in the MINITAB worksheet
workhours.mtw. There is a two page limit on this question.
a. To determine whether there are significant differences between the mean number of
hours worked for the five different types of employee, carry out an appropriate
hypothesis test (a global test) using a significance level of 5%. Do not carry out any
multiple comparisons in this part of the question.
b. The human resources manager needs to employ a new secretary and, as such, asks
the statistical analyst to compare the mean number of hours worked by secretaries
with each of the other four types of employees. Carry out the appropriate hypothesis
tests using an overall significance level of 5%. Summarise your results in a table.
Make sure you indicate the per comparison error rate and the degrees of freedom for
each of these comparisons?
c. Summarise your findings briefly for the human resources manager from the
comparisons carried out in part b. above.
d. Now, using Tukey’s multiple comparisons, write a paragraph summarising the
differences between the numbers of hours worked between the five different types of
employees (ie. all pairwise comparisons) using an overall significance level of 5%.
e. In part b., Bonferroni comparisons were used because we did not make all pairwise
comparisons. Explain why this is better than Tukey comparisons in this situation.
Question 3 (13 marks)
Research Question: Is there evidence of an association between the preferred colour of car
and the country to which they are exported?
You should address the Research Question outlined above. Your answer to this question
should consist of two word-processed pages presented in the form of a statistical report.
The report as outlined below should be provided on the first page with any appropriate
MINITAB output provided on the second page.
A Japanese motor car company has been selling its standard sedan car to Australia, New
Zealand and Singapore for a number of years. For future manufacturing purposes the
company surveys 100 people from each of the three countries and asks them to choose their
preferred car colour from the colours currently offered in the sedan model.
Source: Black, K. et al, “Australasian Business Statistics”. Wiley 2013.
Directions for report writing are given below. More information on report writing, as well as a
sample report is provided on iLearn in the Resources folder. Use the MINITAB file
sedancars.mtw to answer this question. There is a two page limit on this question.
Introduction: State the research question and any background information including why
the study is being conducted. The target population should be made clear.
Methods: Provide a description of the sample used and the variable/s considered. Indicate
the statistical test being used and the reason for using it. This should also include a
comment on the underlying assumptions of the test. Mention any concerns. If the study is
experimental, the design of the experiment should be outlined.
Results: Outline the results from your analyses including the test statistic/s and p-value/s.
You should also clearly state whether or not your result/s are statistically significant.
Conclusion: This should summarise the overall findings of your study. It should address
the research question and include any appropriate confidence intervals.