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HI6007 Statistics for Business Decisions Assignment - Holmes Institute, Australia

Purpose - This assignment is designed to assess your level of knowledge of the key topics covered in this unit.

Unit Learning Outcomes Assessed -

1. Understand appropriate business research methodologies and how to apply them to support decision-making process.

2. Understand various qualitative and quantitative research methodologies and techniques.

3. Explain how statistical techniques can solve business problems;

4. Identify and evaluate valid statistical techniques in a given scenario to solve business problems;

5. Explain and justify the results of a statistical analysis in the context of critical reasoning for a business problem solving.

6. Apply statistical knowledge to summarize data graphically and statistically, either manually or via a computer package;

7. Justify and interpret statistical/analytical scenarios that best fits business solution;

8. Explain and justify value and limitations of the statistical techniques to business decision making and;

9. Explain how statistical techniques can be used in research and trade publication.

Tutorial Questions -

Question 1 - a. The following data shows the results for 20 students in one of the post graduate unit.

42	66	67	71	78	62	61	76	71	67
61	64	61	54	83	63	68	69	81	53

Based on the information given you are required to

i. Compute the mean, median and mode.

ii. Compute the first and third quartiles.

iii. Compute and interpret the 90^th percentile.

b. In your own word, explain what is inferential statistics with relevant examples.

Question 2 - a. Holmes Institute conducted a survey about International Students in Melbourne. The survey results are given in the table below.

		Applied to more than 1 university
		Yes	No
Age Group	23 and under	207	201
	24-26	299	379
	27-30	185	268
	31-35	66	193
	36 and over	51	169

i. Prepare a joint probability table.

ii. Given that a student applied to more than 1 university, what is the probability that the student is 24-26 years old.

iii. Is the number of universities applied to independent of student age? Explain.

b. Assume, North Origano, is a country with highest domestic violence cases (approximately 5 cases per 1000 families). Working with counselors, a researcher developed the following probability distribution for x= the number of new clients for counseling for 2021.

x	f(x)
10	0.05
20	0.10
30	0.10
40	0.20
50	0.35
60	0.20

i. Compute the expected value and variance of x.

Question 3 - According to the Annual survey of drugs expenditure in country X, the annual expenditure for prescription drugs is $838 per person in the Northeast region of the country. A sample of 60 individuals in the Midwest shows a per person expenditure for prescription drugs of $745. Further, it is given that the population standard deviation of $300.

I. Formulate hypotheses for a test to determine whether the sample data support the conclusion that the population annual expenditure for prescription drugs per person is lower in the Midwest than in the Northeast and Identify whether it is a two-tail test or a one tail test (Left or right tail).

II. Decide the suitable test statistics and justify your selection.

III. Calculate the value of the relevant test statistics and identify the P value.

IV. Based on the p value in part (III), at 99% confidence level, decide the decision criteria.

V. Make the final conclusion based on the analysis.

Question 4 - The gasoline price often varies a great deal across different regions across country X. The following data show the price per gallon for regular gasoline for a random sample of gasoline service station for three major brands of gasoline (A, B and C) located in 10 metropolitan areas across the country X.

A	B	C
3.77	3.83	3.78
3.72	3.83	3.87
3.87	3.85	3.89
3.76	3.77	3.79
3.83	3.84	3.87
3.85	3.84	3.87
3.93	4.04	3.99
3.79	3.78	3.79
3.78	3.84	3.79
3.81	3.84	3.86

a. State the null and alternative hypothesis for single factor ANOVA to test for any significant difference in the mean price of gasoline for the three brands.

b. State the decision rule at 5% significance level.

c. Calculate the test statistic.

d. Based on the calculated test statistics decide whether any significant difference in the mean price of gasoline for three bands.

Note: No excel ANOVA output allowed. Students need to show all the steps in calculations.

Question 5 - Dex Research Limited conducted a research to investigate consumer characteristics that can be used to predict the amount charged by credit card users. The following multiple regression output is based on a data collected by this research company on annual income, household size and annual credit card charges for a sample if 50 consumers.

Regression Statistics
Multiple R	0.9086
R Square	A
Adjusted R Square	0.8181
Standard Error	398.0910
Observations	B

ANOVA

	df	SS	MS	F	Significance F
Regression	2	D	E	G	1.50876E-18
Residual	C	7448393.148	F
Total	49	42699148.82

 

	Coefficients	Standard Error	t Stat	P-value
Intercept	1304.9048	197.6548	6.6019	3.28664E-08
Income ($1000s)	33.1330	3.9679	H	7.68206E-11
Household Size	356.2959	33.2009	10.7315	3.12342E-14

a. Complete the missing entries from A to H in this output.

b. Estimate the annual credit card charges for a three-person household with an annual income of $40,000.

c. Did the estimated regression equation provide a good fit to the data? Explain.

Question 6 - Amex PLC has gathered following information on the sales of face mask from April 2020 to September 2020.

Month	Sales ($)
April	17,000
May	18,000
June	19,500
July	22,000
August	21,000
September	23,000

You are required to;

a. Using linear trend equation forecast the sales of face masks for October 2020.

b. Calculate the forecasted sales difference if you use 3-period weighted moving average designed with the following weights: July 0.2, August 0.3 and September 0.5.