Topic

Statistical Analysis To Support Decision Making

Instructions

CASE PROBLEM: Heavenly Chocolates.
Due to ongoing production problems, Heavenly Chocolates’ management has decided to postpone
any plans for a second store/production facility. Instead, they have realised that current production
could be improved by various process improvement activities. They are even considering purchasing
some sophisticated statistical software aimed at their type of industry
(http://www.camo.com/resources/casestudies/Process_Quality_Food_Manufacturing_Nidar.pdf).
Here, only a couple of aspects are investigated.
The Excel file contains random samples from production runs of 150g packets, one for 70% and one
for 85% cocoa chocolate.

1) Various production problems may lead to unplanned downtime. Operators were asked to time
such delays for a week, and record the total minutes against each cause. Below is a table with the
results:
Cause Time (minutes)
Cocoa feeder issue 120
Excess of sugar coating 15
Mixer problem 40
Operator missing 20
Packaging issue 25
Sugar feeder issue 95

Provide an appropriate graph for this dataset, as well as a comment for Management.
(3 marks)

2) The actual weight of packets of a nominal size is subject to variation. To avoid customer
complaints, process targets are set slightly above nominal. For example, 150g packets have
historically had a process target of 156g.
a) Assuming normally distributed packet weights and using the Empirical Rule, what percentage
of packets would be underweight if the standard deviation is 2g? (1 mark)
b) Using the utility at statstar.io, find (by trial and error) the process target that would instead
allow approximately 5% of packets to be underweight. Provide the relevant graph.
(3 marks)

3) Management has a perception that dark chocolate is less liked by women than by men. They
decide to perform a quick survey by asking their employees for their own preference and that of
their family members. The combined results are as follows:
Males Females
Milk 24 41
Dark 20 11

a) What would be the use of knowing about such a relationship? (2 marks)
b) How would you describe the sampling this survey was based on, and what could be an issue
with it? (2 marks)
c) Perform a hypothesis test, at the 5% significance level, to see if there is a relationship
between gender and preference for dark vs milk chocolate. Provide the relevant graph.
(6 marks)

4) In the dark chocolate line, the 150g packet with 70% cocoa is the main product. A random
sample of 100 packets was taken over a week.
a) Provide a graphical display of the weights of these 100 packets and briefly describe the
distribution. (4 marks)
b) Comment on the setting of the process target of 156g, based on an assumed (historical)
standard deviation of 2g. (2 marks)
c) Formally test, at the 1% significance level, whether the process target of 156g was achieved
during the week’s production, in terms of the population mean weight. (5 marks)
d) Also produce a 99% confidence interval for the population mean weight of the week’s
production, and interpret it. (3 marks)
e) Explain how the results at c) and d) are related. (2 marks)

5) In the same chocolate line, 85% cocoa chocolate is less popular with customers. But also,
operators have complained that the lower sugar level potentially leads to underweight packets,
due to inaccurate mixing, compared with the standard 70% cocoa chocolate packets. (A random
sample of 100 packets was taken from an 85% cocoa chocolate production run also.)
a) Provide the appropriate graphical display to compare the 85% and 70% cocoa chocolate
packets, and give a brief description of how the weights compare. (4 marks)
b) Perform a hypothesis test, at the 1% significance level, to test for a difference in means
between 85% and 70% cocoa chocolate packets (150g). (6 marks)
c) A difference of one standard deviation between comparable means is often considered
substantial. Use a 99% confidence interval to test whether the population means of 85% and
70% cocoa chocolate packets (150g) are different by more than 2g. (5 marks)

6) What could be one of Heavenly Chocolates’ aims to produce their chocolates more cheaply?
(2 marks)

Answer preview

The information is used in knowing how to market their product. Places where by we are expecting more male customers more dark chocolates should be sold. When the market is comprised of many ladies more milk chocolates should be supplied. Generally, this information will help in ensuring that supply of the chocolates is made appropriately in relation to the gender of target market.
The sampling used in this study is random since all respondents were given equal chance to be selected. The sampling was done without replacement. The only issue with this mode of sampling is that there are chances of replication of ideas. This will give wrong information of the data accuracy. Also, there are chances of the sampling on wholly representing the whole population.
In this case, the null and alternative hypothesis are: –

Null: there is significant differences between gender and preference for dark and milk chocolate.

Alternative: there is no significant difference between gender and preference for dark and milk chocolate.

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