Major Assignment 2: Probability & Hypothesis Testing Case Study
2024/10/1 14:03 Major Assignment 2: Probability & Hypothesis Testing Case Study
Major Assignment 2: Probability & Hypothesis Testing Case Study
Start Assignment
Due 6 Oct by 23:59
Points 100
Submitting a file upload Available until 6 Oct at 23:59
Overview
This assessment will allow you to apply your newly developed statistical skills to draw conclusions about a population from samples.
This assessment maps to the following Course Learning Outcomes:
1. Apply a variety of statistical techniques, both descriptive and inferential, correctly.
2. Interpret, in plain language, the application and outcomes of statistical techniques.
Due date: End of Week 9 (Sunday, 6 October 2024, by 11:59 pm) Weighting: 10%
Length: Not more than 1200 words
Scenario
You are the manager of a well-established supermarket chain with multiple business operations, including a popular retail store and a factory that produces essential goods. As part of your role, you regularly analyse business data to make informed decisions and optimise performance, leveraging statistical tools and insights.
In this case study, you will tackle several challenges commonly faced by supermarket managers. You will assess customer traffic, analyse purchasing behaviours, manage product offerings, and evaluate the impact of new promotions and pricing strategies. Your ultimate goal is to drive business growth, improve efficiency, and maintain high levels of customer satisfaction.
Questions
Using the information above, go through the steps to answer the following questions, and ensure you explain your answers by commenting on the choice and appropriateness of the test/methodology used in your calculations.
Question 1:
Based on historical data, your supermarket receives an average of 322 customers per day, with a standard deviation of 81 customers per day. Assume the number of customers per day is normally distributed.
What is the probability (to 4 decimal places) that on a given day, the number of customers visiting the supermarket is less than 200? (10 points)
20% of the time, your supermarket will receive more than how many customers in a day? (10 points)
What is the probability (to 4 decimal places) that the average number of customers per day over a
30-day period is between 300 and 333? (10 points)
Question 2:
The CEO claims that 26% of customers who enter the store purchase milk or bread. A survey of 320 customers found that 71 purchased either bread or milk. Assuming the CEO's claim is accurate, calculate the probability (to 4 decimal places) that the sample proportion is no greater than the proportion found in the survey. Based on this probability, what can you conclude about the CEO’s claim? Note: You do not need to formally test the validity of the claim (but you may choose to if you wish). (15 points)
Question 3:
You operate a factory that produces milk to be sold in your supermarket. A quality control check was conducted to ensure that all milk bottles contain the correct amount of milk. A sample of 100 bottles showed an average volume of 2.17 litres, with a standard deviation of 0.2576 litres.
Calculate the 95% confidence interval for the mean volume of all milk bottles (in litres). (10 points)
Determine the minimum number of milk bottles that must be checked to be 86% confident that the
estimate of the average volume is within 0.05 litres of the overall mean volume. (10 points)
Assuming that the volume is normally distributed and that the standard deviation from the quality control check is a reliable estimate of the population standard deviation (σ = 0.2576 litres), does your answer to part b) change? (5 points)
Question 4:
You plan to run a promotion for household products and aim to determine whether it leads to an increase in overall profit. It is known that before the promotion, your supermarket’s average hourly profit was $587.50, with a standard deviation of $35. You intend to test the profit data after implementing the new pricing scheme using a random sample of 48 hours of operation. You are willing to accept a Type I error probability of 0.05.
If the average hourly profit from the sample is $596, should the null hypothesis be rejected for this test? (20 points)
Disregarding your answer for part a), if the null hypothesis is rejected in this test, can it be concluded that the promotion has increased the profit per hour at the 5% significance level? (5 points)
Would your answer to part a) change if you were willing to accept a Type I error probability of 0.1? (5 points)
Submission requirements
Please submit your assignment online on MyUni before the deadline.
You can submit the assignment as often as you want; the last version submitted will be marked as the definitive version. You are encouraged to submit drafts early so as to avoid missing the submission deadline completely and to receive at least partial credit.
Submit your answer by uploading one file with your answers and explanations. The file must be a PDF document. The document must be typed and NOT exceed 1200 words.
You are expected to provide explanations and justifications for every answer. This includes explaining every step of your reasoning, all relevant calculations, and all necessary formulas and mathematical notation. Please clearly indicate when you start the answer for a new question.
Writing the explanations and formulas might require using Greek letters and mathematical expressions. If you encounter difficulties, you may include individual formulas as images (but not any other text).
Calculations can be made in Excel or any other spreadsheet software, as long as a sufficient explanation is provided in the submitted PDF file. Submitting the Excel file is not required, but retaining the file for academic integrity purposes is strongly recommended.
Assessment 2: Probability & Hypothesis Testing Case Study (2024 Sem 2)
Criteria Ratings Pts | ||||||
Question 1A | 10 to >5.0 Pts Meets expectations You have correctly calculated the probability for a given day and clearly explained your method. | 5 to >0 Pts You have not correctly calculated the probability and explained your method. | 10 pts | |||
Question 1B | 10 to >5.0 Pts Meets expectations You have correctly calculated the number of customers and clearly explained your method. | 5 to >0 Pts You have not correctly calculated the number of customers and explained your method. | 10 pts | |||
Question 1C | 10 to >5.0 Pts Meets expectations You have correctly calculated the probability for a 30-day period and clearly explained your method. | 5 to >0 Pts You have not correctly calculated the probability and explained your method. | 10 pts | |||
Question 2 | 15 to >10.0 Pts Meets expectations You have correctly calculated the probability based on the sample provided and clearly explained your method and conclusion. | 10 to >7.5 Pts Meets expectations You have correctly calculated the probability based on the sample provided. However, you have not correctly explained your method or your conclusion. | 7.5 to >0 Pts Doesn't meet expectations You have not correctly calculated the probability and explained your method and conclusion. | 15 pts | ||
Question 3A | 10 to >5.0 Pts Meets expectations You have correctly calculated the confidence interval estimate and clearly explained your method. | 5 to >0 Pts You have not correctly calculated the confidence interval estimate and explained your method. | 10 pts | |||
Question 3B | 10 to >5.0 Pts Meets expectations You have correctly calculated the minimum number of milk bottles and clearly explained your method. | 5 to >0 Pts You have not correctly calculated the minimum number of milk bottles and explained your method. | 10 pts | |||
Question 3C
5 to >2.5 Pts
Meets expectations
You have correctly calculated the minimum number of milk bottles using the population
2.5 to >0 Pts
Doesn't meet expectations
You have not correctly calculated the minimum number of milk bottles using the
5 pts
Criteria
Ratings Pts
population standard deviation and compared the results.
standard deviation and included a clear comparison of the results.
Question 4A | 20 to >15.0 Pts Meets expectations You have correctly conducted the test and clearly explained your steps. | 15 to >10.0 Pts Meets expectations You have correctly conducted the test. However, you have not clearly explained your method or your conclusion. | 10 to >0 Pts Doesn't meet expectations You have not correctly conducted the test and explained your method and conclusion. | 20 pts | |
Question 4B | 5 to >2.5 Pts You have correctly interpreted the rejection decision. | 2.5 to >0 Pts You have not correctly interpreted the rejection decision. | 5 pts | ||
Question 4C | 5 to >2.5 Pts You have correctly explained your conclusion and compared the results. | 2.5 to >0 Pts You have not correctly explained your conclusion and compared the results. | 5 pts | ||
Total points: 100
