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Show correct formulae and/or show appropriate Excel functions with parameters.
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Meet minimum presentation standards expected of a business professional.
Submitted on or before the due date.
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Question 1 – (Total: 60 Marks)
You are the manager of a small business with a contract to maintain and repair Whizo coffee machines. You want to set your new service prices, and you think there may be a relationship between the age of the coffee machine and the number of callouts for repair. If it exists, you want the new prices to reflect such a relationship. You have a record of the age of all the coffee machines on your client list and the number of callouts from each client over the last three months.
Age of machine
Maintenance call outs
(in months)
(numbers of callouts)
24
3
6
5
54
7
6
1
28
1
96
6
90
7
12
1
100
5
84
4
20
2
14
1
54
3
58
4
70
7
36
2
12
1
30
3
24
1
3
0
76
5
105
7
26
2
8
1
38
2
62
4
6
2
44
3
76
5
41
2
Using the data on the age of the coffee machines, determine the mean, median, and standard deviation of their age using ungrouped data methods (i.e., from the raw data). You need to show all the relevant workings by using the appropriate formulas.
[6 marks]
Explain how you would know if a data set is skewed and, in this case, determine whether the “age of the machine” data is skewed.
[3 marks]
Form a frequency distribution table for the “age of the machine” data, comprising 6 classes, starting with “0 &U 20”. For each class, indicate a class mark and then construct a fully labelled histogram using the frequency distribution.
[8 marks]
Using the frequency distribution table in part (c), determine the grouped data's mean, median and standard deviation. You need to show all the relevant workings by using the appropriate formulas.
[8 marks]
Comment on the results (mean, median and standard deviation) obtained in part (a) and part
(c) on the ungrouped and grouped data, respectively. Be sure to explain which are the more accurate.
[4 marks]
Calculate the probability that the age of a randomly chosen machine is 20 months or less.
[4 marks]
Using Excel, create a scattergram of the variables age of machine and number of callouts. Comment on the feasibility of a linear relationship between age and number of call outs.
[4 marks]
Estimate the regression equation that explains the number of callouts by the age of the coffee machine. Here, you are required to show the calculations for the intercept term and the slope coefficient.
[9 marks]
Interpret the slope coefficient and the intercept term for this regression equation, noting any assumptions required for the latter.
[4 marks]
Calculate the standard error of the estimate and the coefficient of determination using appropriate formulas and interpret the values obtained. Show all relevant workings.
[8 marks]
Suppose you have taken on a new client who has a machine that is 10 years old. Explain if you can predict with any confidence the number of callouts for this particular machine?
[2 marks]
Question 2 (20 marks)
The enterprise effectiveness group in a large corporation conducts an audit of business improvement projects. They find that across the business, three different approaches to business improvement are used, namely:
Six Sigma
An internally created methodology called T[do]
A set of proprietary methodologies for which consulting companies own the intellectual property.
It is reported that 70% of the projects use proprietary methodologies, 21% use Six Sigma, and the remainder use T[do].
Each approach involves an initial investigation, which results in a “case for change” document. The document is considered by a gating committee, which decides whether to release funds to continue the project.
The audit group finds that only 40% of investigations gain the funding to continue, meaning that 60% of investigation effort is effectively wasted.
Additional information was provided: 24% of the projects pass the gate and use proprietary methodologies, while 9% pass the gate and use Six Sigma.
Construct a contingency table and show the marginal and joint probabilities that can be derived from the paragraphs above.
[8 marks]
Determine the probability that a randomly selected business improvement project will pass gating if they use:
Proprietary methodologies.
A Six Sigma approach.
T[do].
[9 marks]
Using your results in part (b), explain which approach appears least wasteful of the investigation effort. What other information might cause you to come to a different conclusion?
[3 marks]
The manufacturers of children’s snack bars wish to understand whether their target market prefers products which use sugar as a sweetener compared to Aspartame and Saccharin. They produce three test batches of Bernie Bars, each batch identical except for the sweetener. In a blind test, twelve children between the ages of 5 and 10 are asked to identify which bar they prefer.
If children are not capable of discerning between the taste of the three bars, determine the probability of having six or more choose the bar containing sugar. (Hint: If they can’t discern a difference, assume that they are making a random selection and that the chance of picking a bar containing sugar is 1/3.). Show all relevant calculations.
[5 marks]
Interpret your result from part (a), explaining whether it provides strong evidence that children prefer Bernie Bars, which contain sugar.
[2 marks]
They repeat the experiment on a larger scale, using 40 testers. If children are not capable of discerning between the taste of the three bars, using the appropriate Excel function, determine the probability of having 20 or more choose the bar containing sugar. Interpret your result, explaining whether it provides strong evidence that children prefer Bernie Bars, which contain sugar. Show the Excel functions used to obtain the results.
[8 marks]
Explain why your conclusions in (b) and (c) were different even though both experiments are similar.
[3 marks]
In the country of Britania, the National Weights and Measures Authority (NWMA) has the right to conduct spot checks of food packing operations. Today, they are checking a batch of 256 bags of flour packaged by FlourMill, which are labelled “average contents 10 kg”.
Rather than weigh the contents of every bag, the NWMA weighs a random sample of 24 bags from the batch. The mean weight of the bags is 9.963 kg, with a standard deviation of 0.171 kg.
Test with α = 0.05 whether FlourMill are under-filling their 10kg bags of flour. Please show the seven steps of hypothesis testing. Make sure to state your conclusions and any assumptions that you need to make.
[8 marks]
Using this question as an example, explain the difference between a Type 1 and Type 2 error.
[3 marks]
Six of the 24 bags sampled had blurry printing on the bag. Find the 95% confidence interval for the proportion of bags in the batch with blurry printing.
