**1305AFE Business Data Analysis Problem-Solving Assignment**

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**Assessment Details:-**

**Course Title: Business Data Analysis****Course Code: 1305AFE****Words: 5000****Deadline: As Per Required**

**Assessment Task:-**

*Problem 1 – Assembly time in a factory***(6 marks)**

The operation manager of a large factory in China wishes to implement a quality control in the assembly process of a sub-component of a plasma television. Such control is believed to enhance workers’ efficiency. This will then lead to an improvement in profit. The amount of time required to assemble the sub-component is normally distributed, with a mean of 15 minutes and a standard deviation of 1.8 minutes.

- What is the probability that one randomly selected assembly would take at most 17 minutes to complete? Display working.
**(1 mark)** - The 10% assemblies which take the longest to complete would at least require how much time (in minutes)?Display working.
**(2 marks)** - The operation manager randomly selected seven assemblies. What is the probability that the mean amount of time taken to complete those seven assemblies is more than 15.6 minutes? Display working.
**(1.5 marks)** - In further implementing the quality control, eight other assemblies are randomly selected. What is the probability that the average amount of time to complete those eight assemblies is between 15 minutes and 16 minutes? Display working.
**(1.5 marks)**

*Problem 2 – Keeping the border closed* (10 marks)

Western Australia is a state that occupies the western 32.9% of the land area in Australia, excluding the external territories. It is estimated to have about 2.6 million inhabitants. The state is very cautious in protecting its residents from the transmission of the Covid-19 infection. Hence, it imposed a tough regulation to close its borders from other states which had recorded an increased number in Covid-19 infection. The residents however have mixed reactions to the regulation. Some were supportive to the regulation. Others argue that opening the state border should be made a priority to boost the economy. A survey on the matter is conducted over 3,000 randomly selected residents where they are asked to cast their vote (‘SUPPORT’ or ‘NOT SUPPORT’ on the decision to remain in closing the border). 1,680 respondents stated ‘SUPPORT’ for the state to remain closed.

- Suppose you were adata analyst working for the State Office of Statistics. Assist the office in performing a hypothesis test at the 5% level of significance to infer whether more than 55% of Western Australian residents support for the state border to remain closed. Display the six-steps process (involving drawing the rejection region/s and determining the critical value/s for the decision rule) in performing the test.
**(6 marks)** - Specify the decision rule to use in the p-value method hypothesis testing. Calculate the p-value of the test above. Display working.
**(2 marks)** - Which one of these two types of error (i.eType I or Type II) you could make with the conclusion you made in part a)? Briefly explain the reasoning for your selection.
**(1 mark)** - What is the required condition for ensuring that the sampling distribution of the sample proportion is approximately normally distributed? Check if the condition is satisfied in the hypothesis testing that you just completed.
**(1 mark)**

*Problem 3 – Retail price investigation (8 marks)*

TMS is a brand of designer T-shirts that is highly popular amongst the teenagers. The manufacturer suspects that its retailers charge less than the recommended retail price of $60. A market research company was engaged to investigate the matter and collected data from 66 randomly selected retailers. The mean retail price calculated from the sample is found to be $59 with a standard deviation $5.20. Assuming that retail prices of the T-shirts are normally distributed, estimate with 95% confidence the actual mean retail price of the T-shirts.

- Suppose you were a junior statistician working for the market research company. Which formula would you select to use in solving the problem? Provide a brief reason on your selection.
**(1 mark)** - Obtain the lower confidence limit and the upper confidence limit of the 95% confidence interval estimate of the actual mean retail price of the T-shirts. Display working.
**(3 marks)** - Present an interpretation of the lower confidence limit and the upper confidence limit obtained in part b) in the context of the problem.
**(5 marks)** - Does the result of the estimation you just completed fully support the suspicion of the manufacturer? Yes or no? Why? Present your reasoning.
**(5 marks)** - What would happen to the width of the interval when a higher confidence level is used? Assumeall of the other variables to do the calculation of confidence interval held constant.
**(1 mark)**

*Problem 4 – Consumer behaviour theory (16 marks)*

*“Consumers are likely to purchase more of a good when the price of the good decreases, and vice versa.” *

As stated above, a marketing theory in the field of consumer behaviourbelieves that an indirect relation is likely to exist between the price and the number of units purchased for most of the goods and services. In examining this, you were commissioned as a student in the Business Data Analysis course to conduct a mock market research surveying a sample of potential customers in purchasing a hypothetical new product. You randomly selected 15 of your fellow students as the potential customers for the product. You questioned them on the number of units they were likely to purchase for a given price that you set. The data you collected from the mock survey are displayed below. You are tasked in performing therelevant inferential analyses on the relation between the two concerned variables by addressing the below set of questions.

Potential Customer | Set Price | |

Number of units | ||

purchased | ||

in $ |
||

Jim | 13 | 20 |

Jack | 20 | 17 |

John | 13.5 | 21 |

Pete | 14 | 19 |

Sam | 17.2 | 14 |

Andy | 18 | 15 |

Winnie | 15 | 15 |

Amanda | 16.3 | 14 |

Dale | 16.5 | 13 |

Naomi | 17 | 11 |

Kim | 14.2 | 17 |

Megan | 15 | 13 |

Jennie | 19 | 15 |

Jill | 19.5 | 16 |

Bill | 13 | 22 |

- Which of the two concerned variables is the dependent variable? Which one is the independent variable? Give an explanation of the rationale of the selection of the dependent and independent variables.
**(1 mark)** - The following sums have been computed:

∑X_i =241.2 ∑Y_i =242 ∑X_i Y_i= 3834.4

∑X_i^2 =3955.92 ∑Y_i^2 =4046

Use this info to calculate S_{x}^{2}, S_{y}^{2}and S_{xy}. Display working.**(1.5 marks)** - Calculate the sample correlation coefficient. Display working. Then, provide an interpretation of the calculated correlation in terms of the relation between price and number of units purchased.
**(2 marks)** - Calculate the slope coefficient of thesample linear regression. Then, calculate the intercept coefficient of the sample linear regression. Display working.
**(1 mark)** - Write the estimated sample linear regression equation.
**(1 mark)** - Provide interpretations of the slope coefficient and the intercept coefficient of the sample linear regression in terms of the relation between price and number of units purchased.
**(2.5 marks)** - Predict the number of units purchased if price is $23. Display working. Comment on the validity of this prediction.
**(2 marks)** - Calculate the coefficient of determination for the regression line.Provide an interpretation of the calculated coefficient of determination in terms of the relation between price and number of units purchased.
**(2 marks)** - Performtherelevant hypothesis test at the1% level of significance to see if a negative relation exists between price and number of units purchased. Display working of the six-stepsof the hypothesis test. The t test-statistic has been calculated. t calculated = -2.34.
**(3 marks)**

**—-End of Assignment—**

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