Problem 1 - Efficiency analysis of workflow system(8 marks)

John is the Chief Financial Officer of a very large software company that employs more than 5,000 programmers.He is committed to increase funding to the development of the company's new workflow system if at least 20% of his programmers agree that the system significantly enhances their work efficiency.700 programmers were randomly selected and surveyed for this analysis.175 programmers stated that they find the workflow system is useful and boost their work efficiency.Estimate with 99% confidence the proportion of all of the company's programmers who find the new workflow system useful for their work efficiency.

a)Suppose you were a researcher working for the data analytic department of the company.Which formula would you select in solving the problem?Provide a brief reason on your selection.1 mark

b)Obtain the lower confidence limit and the upper confidence limit of the 99% confidence interval estimate of the proportion of all the company's programmers who find the new workflow system useful for their work efficiency.Display working.3 marks

c)Present an interpretation of the lower confidence limit and the upper confidence limit obtained in part b) in the context of the problem.1.5 marks

d)Based on the interval estimation you just conducted, present brief statements of two or three sentences for John, the Chief Financial Officer.Should he allocate more funding for the development of the company's new workflow system? Yes or no? Why?1.5 marks

e)What would happen to the width of the interval when a lower sample size is used?Assume all of the other variables to do the calculation of confidence interval held constant. 1 mark

Problem 2 - Used car price evaluation(10 marks)

It is estimated that around 13% of the residents of Jakarta use cars to commute.Despite the current Covid-19 pandemic, a large car dealership in the city reported that the demand for used mid-size passenger sedans in the city has become stronger.The dealership further claimed that the average selling price for used mid-size passenger sedans is now more than $9,500.In verifying this, a random sample of 120 used mid-size passenger sedans is selected.The average price calculated from the sample is $9,600.Assume that the population standard deviation of the price is $1,200.

a)Suppose you were a junior business analyst working for the dealership.Assist the dealership in performing a hypothesis test at a 10% level of significance to check whether the dealership's claim is supported.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

b)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

c)Which one of these two types of error (i.e Type I or Type II) you could make with the conclusion you made in part a)?Briefly explain your selection. 1 mark

d)What is the required condition for ensuring that the sampling distribution of the sample mean is approximately normally distributed?Check if the condition is satisfied in the hypothesis testing that you just completed.1 mark

Problem 3 - 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 behaviour believes 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 16 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 the relevant 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 $

Matt

13

21

Kim

15

15

Ken

13.5

21

Tom

15

13

Tim

16.5

14

Anne

13.5

22

Will

14

19

Joe

14.2

17

Jim

16.5

13

Naomi

17

13

Mike

17.2

14

Megan

18

15

Jennie

20

17

Andy

21

14

Bill

19

17

Tony

19.5

16

a)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)

b)The following sums have been computed:

Use this info to calculate S_x², S_y² and S_xy.Display working.

(1.5 marks)

c)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)

d)Calculate the slope coefficient of the sample linear regression.Then, calculate the intercept coefficient of the sample linear regression. Display working.(1 mark)

e)Write the estimated sample linear regression equation. (1 mark)

f)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)

g)Predict the number of units purchased if price is $25.Display working.Comment on the validity of this prediction.(2 marks)

h)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)

i)Perform the relevant hypothesis test at the 5% level of significance to see if a negative relation exists between price and number of units purchased.Display working of the six-steps of the hypothesis test.The t test-statistic has been calculated.t calculated = -2.35.

(3 marks)

Problem 4 - Time spent for meeting during Covid(6 marks)

A newspaper report stated that the hours spent by office workers in attending meetings have increased substantially during Covid-19.A study is conducted to examine the amount of time that office workers spend in attending meetings per week during the pandemic.The amount of time that office workers spend in attending meetings per week during Covid is normally distributed with a mean of 9 hours and a standard deviation of 1.5 hours.

a)What is the probability that one randomly selected office worker would spend more than 6 hours per week for meetings? Display working.1 mark

b)At most how much time per week (in hours) would be used by the 3% office workers who spend the shortest amount of time for meetings? Display working.

2 marks

c)An analyst randomly selected five office workers.What is the probability that the mean amount of time per week spent for meetings for those five workers is less than 11 hours per week?Display working.

1.5 marks

d)Further, the analyst randomly selected four other office workers.What is the probability that the average amount of time per week spent for meetings for those four workers is between 8 hours and 10.5 hours? Display working.