1. True or False: Mark each statement True or False. Please explain.
a) For a simple regression, if the Adjusted R-sq is only 5%, then the coefficient corresponding to the independent variable cannot be statistically significant.
2. Probability Distribution: In finance, the acronym VaR stands for "value at risk". J. P. Morgan introduced value at risk in the 1980s as a way to answer a common question asked by investors: "How much might I lose?" VaR works by using a probability model to rule out the 5% worst things that might happen over a specified time horizon, such as the next year. For example, if a portfolio of stocks has an annual 5% VaR of $0.6 million, there is a 5% probability that the value of the portfolio will drop by more than $0.6 million over the next year. Any probability model can be used to compute VaR.
Imagine that you manage the $10 million portfolio of a wealthy investor. The portfolio is expected to average 10% return over the next year with standard deviation 20%.
a) If the annual return of the portfolio follows a t-distribution with five degree of freedom (d.f. = 5), and with the same mean and standard deviation as above, then what is the annual VaR for this portfolio?
3. Sampling and Confidence Interval: NEXNet Corporation is a small but aggressive company in the telecommunications market considering an expansion into the Chicago area, and they are targeting relatively high income communities. Based on previous experience, they have found that they are able to operate profitably in communities where the mean monthly household telephone bill is greater than $75.00.
As part of the analysis of potential communities to target for marketing and sales, NEXNet has arranged for a survey to be conducted for 70 randomly chosen households in a high income community around Chicago. The data of their October telephone bill is in the file Q3_NEXNetl.xlsx.
a) Plot a histogram of the 70 October telephone bills. Does the shape of the distribution of "October phone bills" resembles a Normal Distribution?
b) What is an estimate of the mean and standard deviation of the distribution of October household telephone bills?
c) Based on the data, would you advise NEXNet to enter this community? Does your conclusion depend on any assumption on the shape of the distribution?
4. Hypothesis Testing: Customers with Premier Account visiting the HSBC Baker
Street Branch often complain that they have to wait for an outrageous amount of time before being served. To improve customer satisfaction, the branch manager carefully studied the customer arrival pattern and proposed a plan to rearrange bankers' lunch break in order to reduce customers' waiting time. To evaluate if the plan is effective, the manager first asked an intern to randomly record the waiting time of 15 customers when bankers followed their original schedule (as summarized in the Before Improvement column in the data file Q4_bank.xlsx), and then asked the intern to again randomly record the waiting time of another 15 customers after the proposed plan was implemented (as summarized in the After Improvement column in the data file Q4_bank.xlsx). Using the data, can you help the manager assess if the proposed plan is effective in shortening customers' waiting time?
a) Please state and explain your hypotheses clearly.
b) Carry out the hypothesis test and interpret your results.
c) The manager is concerned that the sample size of 15 is too small to draw any meaningful conclusion. Do you agree with him? Please explain.
Attachment:- Assignment Data.rar