Reference no: EM132765891
HI6007 Statistics for Business Decisions - Holmes Institute
Purpose of the assessment (with ULO Mapping) - Students are required to show understanding of the principles and techniques of business research and statistical analysis taught in the course.
Assignment Specifications -
Purpose: This assignment aims at assessing students' understanding of different qualitative and quantitative research methodologies and techniques. Other purposes are:
1. Explain how statistical techniques can solve business problems.
2. Identify and evaluate valid statistical techniques in a given scenario to solve business problems.
3. Explain and justify the results of a statistical analysis in the context of critical reasoning for a business problem solving.
4. Apply statistical knowledge to summarize data graphically and statistically, either manually or via a computer package.
5. Justify and interpret statistical/analytical scenarios that best fit business solution.
Answer all Questions
Question 1 - A group of researchers conducted a research in order to assess their opinion on expected 20% increase in development tax with the expectation of commencement of a new rail road project. Each person being interviewed was asked whether they would vote for this new change or not. Possible responses were vote for, vote against, and no opinion. 295 respondents said they would vote for the law, 672 said they would vote against the law, and 51 said they had no opinion.
a. Do the responses for this question provide categorical or quantitative data? What is the scale of measurement?
b. Draw a suitable graph and explain whether the results indicate general support for or against increasing the development tax to commence the new rail road project?
Question 2 - ABZ research consultancy firm conducted a study of how chief executive officers (CEOs) spend their day. The study found that CEOs spend on average about 18 hours per week in meetings, not including conference calls, business meals, and public events. Shown below is the time spent per week in meeting (hours) for a sample of 25 CEOs.
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14
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15
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18
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23
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15
|
|
19
|
20
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13
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15
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23
|
|
23
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21
|
15
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20
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21
|
|
16
|
15
|
18
|
18
|
19
|
|
19
|
22
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23
|
21
|
12
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a. Prepare a numerical summary report including the summary measures, mean, median, range, variance, standard deviation, and coefficient of variation, smallest and largest values, and the three quartiles.
b. Use a class width of 2 hours to prepare a frequency distribution and a percentage frequency distribution for the data.
c. Prepare a histogram and comment in the shape of the distribution.
Question 3 - Three group of researchers would like to seek your help to determine the methods of data collection and methods of sampling for the following statistical analysis. Propose the suitable method of data collection and method of sampling for each of the following with sufficient justification why you recommend your selection, over other possible methods.
a. Analyse the voting intention of Australian voters for upcoming election.
b. Investigation of reasons for not Big 4 banks (NAB, ANZ, CBA and WBC) passing on the full interest cuts introduced by reserve bank of Australia to its borrowers.
c. Understand the demographic profile of the community living in Hume city council, Melbourne.
d. Examine opinions from adults on legalising marijuana use in Australia.
e. Estimation of the average age of children in city of Melbourne.
Question 4 - A sample of 15, 10 years -old children was taken to study whether watching television reduces the amount of physical exercise, causing weight gains. The number of kilograms each child was overweight by was recorded (a negative number indicates the child is underweight). In addition, the number of hours of television viewing per week was also recorded. These data are listed in the table below.
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Television(hours)
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42
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34
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25
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35
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37
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38
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31
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33
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19
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29
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38
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28
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29
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36
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18
|
|
Overweight (Kg)
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8
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3
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0
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0
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6
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6
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3
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3
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-4
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4
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4
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2
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1
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6
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-3
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a. Use an appropriate plot to investigate the relationship between Television(hours) and Overweight (KG). Briefly explain the selection of each variable on the X and Y axes and why?
b. Calculate and interpret the coefficient of correlation (r) between Television(hours) and Overweight (KG).
c. Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model.
d. Determine the coefficient of determination (R2) and interpret it.
e. Test the significance of the relationship at the 5% significance level.
f. What is the value of the standard error of the estimate (se). Then, comment on the fitness of the linear regression model?
Note: Answer for question (b) to (f) should be supported with the excel output. Hence, you are required to provide the excel output as the supplementary file(s) in Appendix Section.