Essay XYZ Consumer Protection Authority – The microeconomic theory – Management Assignment Help

Assignment Task:

Assist the researcher in interpreting the outputs by answering these questions. 

1. a)  Provide an interpretation of the reported value of the mean in the context of the problem. 
2. b)  Provide an interpretation of the reported value of the median in the context of the problem. 
3. c)  Provide an interpretation of the reported value of the first quartile in the context of the problem. 
4. d)  If you were to draw the histogram of the data set, what shape of distribution do you think the data collected would resemble? Provide a brief justification to your answer. 

e) Calculate the approximate standard deviation using the relevant formula. Display working. Provideareasononwhytheapproximatestandarddeviationyoucalculated differs substantially to the standard deviation value reported in the table. 

Problem 2 – Re-open for non-essential businesses? 

Queensland is a state with a population of 5.1 million residents. It is reported that Queensland is doing very well in flattening the curve on the number of new cases of the Covid- 19 infection. Queenslanders are divided on whether or not the state to re-open for non- essential businesses. A survey is conducted over 1,500 residents where they are asked to cast their vote on the issue. 1,020 residents stated ‘yes’ for the state to re-open for non-essential businesses. 

1. a)  You were recently hired as a junior statistician working for the Office of the Premier of Queensland. Assist the office in performing a hypothesis test at the 1% level of significance to infer whether more than 65% of Queenslanders agree for the state to re-open for non-essential businesses. 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. 
2. b)  Calculate the p-value of the test above. Display working. State the decision rule should you want to use the p-value method hypothesis testing. 2 marks 
3. c)  This hypothesis test is conducted on the basis that the sampling distribution of the sample proportion is approximately normally distributed. Specify the required condition to ensure this. Further, check if the condition is satisfied. 
4. d)  Identify which one of these two types of error (Type I or Type II) you could make with the conclusion you made in part a). Briefly explain your selection. 

Problem 3 – Weight inspection 

XYZ Consumer Protection Authority (XYZ-CPA) is responsible for enforcing laws concerning weights of advertised essential items. XYZ-CPA routinely inspects packages to determine if the net weight of the contents of 20kg rice bags is at least as large as the net 20kg weight advertised on the bag. 

A random sample of 96 bags were inspected where the net weight content of each of those bags was measured. The mean net weight content calculated from the sample is found to be 20.30kg with a standard deviation 1.20kg. Assuming that the net weight of 20kg rice bags is normally distributed, estimate with 95% confidence the actual mean net weight content of 20kg rice bags. 

1. a)  You were recently hired as a junior data analyst working for XYZ-CPA. Specify the appropriate formula you would use to solve the problem. Provide a brief reason why you chose the formula. 
2. b)  Obtain the 95% confidence interval estimate of the actual mean net weight content of 20kg rice bags. Display working. 
3. c)  Provide an interpretation of the answers you obtained in part b) in the context of the problem. 
4. d)  Present brief statements of two or three sentences to XYZ-CPA with regard to the outcome of the weight inspection or the quality control process that you just conducted. Should the XYZ-CPA be satisfied with the outcome? Yes or no? Why? 

       5. e)  Assuming all of the other variables to do the calculation of confidence interval held constant, what would happen to the width of the interval when a higher sample size is used? 

Problem 4 – Analysis of the law of demand (16 marks) 

The microeconomic theory states that an inverse relation is likely to exist between price and quantity demanded for normal goods. To examine the validity of this theory in the market of apples, a market researcher observed the daily market price of a box of apples and the number of boxes of apples demanded in a local wholesaler fruit market over a period of nine days. By referring to data and additional information displayed below, assist the researcher in performing correlation and simple linear regression analyses on the two variables.

1. a)  State the dependent and independent variables. Briefly explain your selection of the dependent and independent variables. (1 mark) 
2. b)  Calculate Sx2, Sy2 and Sxy using the information given above. Display working. 

       3.c) Calculate the sample correlation coefficient. Display working. 

4. d)  Provide an interpretation of the calculated value of the sample correlation coefficient in terms of the relation between price and quantity demanded. 
5. e)  Calculate the slope coefficient of the sample linear regression equation. Display working. 
6. f)  Provide an interpretation of the slope coefficient you calculated in terms of the relation between price and quantity demanded. 
7. g)  Calculate the intercept coefficient of the sample linear regression equation. Display working. 
8. h)  Provide an interpretation of the intercept coefficient you calculated in terms of the relation b inetween price and quantity demanded. 
9. i)  State the estimated sample linear regression equation. (1 mark) 
10. j)  Predict the quantity demanded if price is $19. Display working. Comment on the validity of this prediction. (2 marks) 
11. k)  Conduct a test on the slope coefficient to see if a negative relation exists between the two variables. Use a 5% level of significance. Display working of the six steps hypothesis test. The t test-statistic has been calculated. It equals -4.40. 
12. l)  Calculate the coefficient of determination for the regression line. 
13. m)  Provide an interpretation of the calculated coefficient of determination in terms of the relation between price and quantity demanded.