Reference no: EM132919671

HI6007 Statistics for Business Decisions - Holmes Institute

Question 1

a. Holmes institute Students evaluation of the course they follow, askes following questions from students. Identify the type of data and measurement scale for each with relevant justifications.
i. How many interactive tutorials did you attend in this semester?
ii. What was your group assignment grade (HD, D, C, P, F)?
iii. Rate the lecturer (very effective, effective, not too effective and not at all effective)
iv. Which campus you are registered in (Melbourne, Sydney, Brisbane or Gold coast)

b. An investor recorded the following annual returns of one of his investments. You are required to calculate and comment on;
i. Mean return.
ii. Variance and standard deviation of the return.
iii. Geometric return.

Year	2016	2017	2018	2019	2020
Return	15%	17%	19%	10%	-5%

Question 2

Nature lovers' association of Australia, launched a campaign to encourage paper less communication and/or recycling of used papers to save the trees to reduce global warming. Hence, many small businesses have scaled up their business such as new forms of online document exchanges and collecting used papers and cardboards from households and companies.
Abita Recycling Ltd is one such company which is operates in Melbourne. The financial analysist of the company has estimated that the firm would make a profit if the mean weekly collection of papers and cardboards from each household exceeded 1KG. To examine the feasibility of a recycling plant, a random sample of 100 households was selected and sample mean and standard deviations are 1.1KG and 0.35KG respectively.

Following the 6-step process of hypothesis testing, you are required to examine do this information provide sufficient evidence at 99% confidence to allow the analyst to conclude that a recycling plant would be profitable?

Question 3

Edex limited is a renowned agricultural chemical manufacturer in Australia. They conduct many research and development in the field of Agri and Horticulture. Company wanted to examine the effect of temperature on farming of their selected range of products.
Company has produced following results based on their data gathering.

15° C	35	24	36	39	32
25° C	30	31	34	23	27
35° C	23	28	28	30	31

You are required to answer following questions;
a. State the null and alternative hypothesis for single factor ANOVA to test for any significant difference in the perception among three groups.

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

c. Calculate the test statistic.

d. Based on the calculated test statistics, decide whether there are any significant differences between the yield based on the given temperature levels.

Note: No excel ANOVA output allowed in question3. Students need to show all the steps in calculations.

Question 4 Melbourne Uni Lodge has decided to provide cup of cold or hot drinks for their tenants to attract them after the Covid pandemic.They have determined that mean number of cups of drinks per day is 2.00 with the standard deviation of 0.6. There will be 125 new tenants in the upcoming months.

What is the probability that the new tenants will consume more than 240 cups of drinks per day?

Question 5 Yummy Lunch Restaurant needs to decide the most profitable location for their business expansion. Marketing manager plans to use a multiple regression model to achieve their target. His model considers yearly revenue as the dependent variable. He found that number of people within 2KM (People), Mean household income(income), no of competitors and price as explanatory variables of company yearly revenue.

The following is the descriptive statistics and regression output from Excel.

	Revenue	People	Income	Competitors	Price
Mean	343965.68	5970.26	41522.96	2.8	5.68
Standard Error	5307.89863	139.0845281	582.1376385	0.142857	0.051030203
Median	345166.5	6032	41339.5	3	5.75
Mode	#N/A	5917	#N/A	3	6
Standard Deviation	37532.51115	983.47613	4116.334718	1.010153	0.360838027
Sample Variance	1408689393	967225.2984	16944211.51	1.020408	0.130204082
Sum	17198284	298513	2076148	140	284
Count	50	50	50	50	50

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.77
R Square	A
Adjusted R Square	B
Standard Error	25139.79
Observations	50.00
ANOVA
	df	SS	MS	F	Significance F
Regression	C	40585376295	F	H	3.0831E-08
Residual	D	28440403984	G
Total	E	69025780279
	Coefficients	Standard Error	t Stat	P-value
Intercept	-68363.1524	78524.7251	-0.8706	0.3886
People	6.4394	3.7051	I	0.0891
Income	7.2723	0.9358	J	0.0000
Competitors	-6709.4320	3818.5426	K	0.0857
Price	15968.7648	10219.0263	L	0.1251

You are required to;
a. Complete the missing entries from A to L in this output

b. Derive the regression model

c. What does the standard error of estimate tell you about the model?

d. Assess the independent variables significance at 5% level (develop hypothesis if necessary in the analysis)?

Question 6

Anita Limited has shared their annual sales revenue over the last 6 financial years from 2015 to 2020.

Year	Sales ($ 000)
2015	4500
2016	5100
2017	4900
2018	5400
2019	5670
2020	6000

You are required to;
a. Using linear trend equation forecast the sales revenue of Anita Limited for 2021.

b. Calculate the forecasted sales difference if you use 3-period weighted moving average designed with the following weights: 2018 (0.1), 2019 (0.3) and 2020(0.6).

Attachment:- STATISTICS FOR BUSINESS DECISIONS.rar