# In real-world decision-making, can we rely on any single method, or do they vary based on the situation for which we need to assign probabilities? Justify your answer.

Question 1 (10 marks)
Probabilities measure the likelihood of the occurrence of events, and in practice, there are different methods to assign probabilities.

Based on the content you learned in in this unit, discuss the main methods used to assign probabilities. (2.5 marks)

In real-world decision-making, can we rely on any single method, or do they vary based on the situation for which we need to assign probabilities? Justify your answer.

(2.5 marks)

Urban Insight Research requires expert advice on selecting optimal sampling plans for their data collection initiatives in the following research scenarios.

Scenario

A research to review the public sentiment regarding COVID-19 annual booster vaccination.

A research to assess the socioeconomic status of residents in rural areas of Victoria, Australia.

Required:

For each scenario, you are required to:

Discuss at least two alternative sampling methods,

Explain the significance of each method in the context of the research,

Describe the sampling process using hypothetical data for both population and sample, and

Identify and justify the most suitable sampling method for the scenario.

(5 marks)

Question 2 (10 marks)
A researcher, Dr. Smith, is conducting a study on the academic performance of students at a local high school. The results of this study will provide valuable insights into the academic performance of students at the high school and inform potential interventions to support student success.

To investigate the average test scores of students, Dr. Smith randomly selects a sample of 8 students from the population of all students at the school. After collecting the data, Dr. Smith calculates the sample mean test score to be 68, with a standard deviation of 50.

Required:

Using the 6-step process of hypothesis testing learned in HM6007, assess whether he would be able to conclude with 90% confidence that the population mean is less than 85. (7 marks)

Innovate Enterprises’ sales team is launching a new product and has initiated a survey of potential customers as a preliminary step.

Required:

Determine the necessary sample size for the company to estimate, with 99% confidence, the proportion of individuals likely to purchase the product within a margin of 3%. (3 marks)

Question 3 (10 marks)
The Smart Kitchen Grocery Store has established multiple outlets across various suburbs in Victoria and anticipates expanding its services to New South Wales. In a bid to ascertain potential variations in sales revenue contingent upon location, considering their presence in Inner CBD, Outer CBD, and regional areas, the store administration opted to conduct an analysis of variance (ANOVA). Subsequently, the ANOVA output is presented for examination. However, One of Junior researcher in your team has mistakenly deleted some observations and they are labelled from A – E.

Anova: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

Store in Inner CBD

10

3860

386

6648.889

Store in Outer CBD

10

3910

391

6276.667

Store in regional Victoria

10

2950

295

2500

ANOVA

Source of Variation

SS

df

MS

F value

F crit

Between Groups

A

B

D

E

3.354131

Within Groups

138830

C

5141.852

Total

197236.7

29

Required:

Using the 6-step process of hypothesis testing learned in this unit, with 95% confidence, decide whether there are any significant differences between the sales across 3 stores.

Question 4 (10 marks)
Transworld Logistics operates their delivery service spanning all states in Australia. The company’s marketing director, Ms. Harper, endeavors to ascertain the principal factors influencing delivery arrival times. To accomplish this, a sample of 50 deliveries was randomly selected for analysis. The dataset encompasses variables including the time taken for delivery arrival (measured in minutes), the total quantity of packages, and the aggregated weight (in hundreds of kilograms).

Following tables shows the regression output of the sample data set.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.836420803

R Square

0.699599759

0.68681677

Standard Error

8.823384264

Observations

50

ANOVA

df

SS

MS

F

Significance F

Regression

2

8521.530836

4260.765

54.72897

0.000000

Residual

47

3659.049164

77.85211

Total

49

12180.58

Coefficients

Standard Error

t Stat

P-value

Intercept

-13.669

7.829028389

-1.74599

0.087346

Packages

0.5172

0.067246763

7.691119

0.000000

Weight

0.2901

0.11166803

2.597671

0.012494

Required:

Determine the multiple regression equation (1 mark)

Assess the goodness of fit of the regression model (2 marks)

Develop hypothesis and assess the independent variables significance at 5% level? (3 marks)

How well does the model fit the data? (2 marks)

v. Propose minimum of 2 new explanatory variables to the model and justify your selection. (2 marks)

Question 5 (10 marks)
A quality control team conducted a study to measure the time it takes to complete a specific quality check in a manufacturing plant. They collected data from a random sample of 18 quality checks and found that the average time was 9.7 minutes, with a standard deviation of 1.5 minutes.

Required:

Assuming that the times are normally distributed, calculate the 99% confidence interval for the mean time required to complete the quality check. (5 marks)