301123 - Management Analytics - Statistics Assignment Help

Assignment Task

Below are all the formulas that were covered in the Topics4 and 5. In the class test, if you use one of these formulas, please just write the formula number; for example, if you were performing a one-sample t-test for the population mean, you would write “formula number 17”.

Question 1 (4 + 2 = 6 marks)

Mr. Jones is attempting to determine where he should invest $100,000 that he has won in a lottery. He has narrowed his choices down to three investment funds a1, a2, and a3. 

The events of interest are the various states of the economy. You have constructed the following payoff table showing the various alternatives, states of nature and payoffs.

(a) Calculate the Expected Profit (EMV) for each possible fund. What fund would you invest in, on the basis of maximising the expected profit?

(b) Calculate the Expected Value of Perfect Information (EVPI) for this decision-making scenario.  

Question 2 (2 + 3 + 2 = 7 marks)

The annual salaries of employees in a large company are approximately normally distributed, with a mean of $50,000 and a standard deviation of $20,000.

(a) What is the probability that an employee earns a salary greater than $100,000?

(b) The company provides free public transport to the employees that earn the lowest 10% of salaries. Less than what salary does a person have to earn to qualify for the free public transport?

(c) A sample of 16 employees is now taken. What is the probability that the sample mean is greater than $40,000?

Question 3 (4 + 2 = 6 marks)

(a) In a sample of 100 items from a production line, 14 are defective. Use these sample data to construct a 99% confidence interval for the true proportion of all items that are defective.

(b) A national survey research firm has past data that indicate that the interview time for a consumer opinion study has a standard deviation of 16 minutes. How large a sample should be taken if the firm wants to estimate the mean interview time to within 2.5 minutes or less with 95% confidence?    

Question 4 (6 marks)

A city planner working on bike tracks needs information about local bicycle commuters. He designs a questionnaire. One of the questions is how many minutes it takes the rider to pedal from home to his or her destination. A random sample of local bicycle commuters yields the following times.

21    19    24    31    29
29    21    15    27    23
38    31    30    26    14
    
Assume that the times are normally distributed. At a 5% level of significance, can we conclude that the mean commuting time of all local bicycle commuters in the city is more than 20 minutes?
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