STAT1060 – ASSESSMENT 1 STATISTICAL ANALYSIS TO SUPPORT DECISION MAKING Total marks: 50; Weight: 20% Due time and date: 23.59AEDT, Sunday end of Week 8 Submission instructions and general...

STAT1060


– ASSESSMENT 1

STATISTICAL ANALYSIS TO SUPPORT DECISION MAKING

Total marks: 50; Weight: 20%

Due time and date: 23.59AEDT, Sunday end of Week 8

Submission instructions and general marking criteria:

1. Submit a soft copy in Word format via Turnitin.

2. Late Submission Penalty: As detailed in the Course Outline.

3. We expect that students will use Excel to assist with calculations and preparation of appropriate graphs, but raw computer output without explanatory text is not acceptable. Answers must be written in clear English sentences clearly linked to all APPROPRIATE supporting computer output. (“Appropriate” means you need to use some judgment. Extract the parts of the Excel output that are relevant to answering the question. Do not include the bits that are not.)

4. You will need to demonstrate understanding of types of data, the use of graphs to explore distributions of variables and relationships between variables, and of statistical tests of such relationships. Marks will be awarded based on the quality of your assessment of the data and how clearly that assessment is communicated.

This


assignment


has

several purposes. It requires you to:

1. Apply concepts from Weeks 1 to 8 to the activities of a specific chosen scenario.

2. Apply the correct analysis to the various scenarios/data sets. Students should be familiar with all types of analysis and corresponding Excel output.

3. Write up the results of a statistical analysis.

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:

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:

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)