Essay Data Analysts have Come into High Demand in the Consulting Industry – Statistics Assignment Help

Assignment Task:

Task:

Problem 1
Data Analysts have come into high demand in the consulting industry in recent times. Candidates possessing a combination of data science, computer, and business seem to be hitting it big with the top firms in the industry. Once these people are hired, they frequently switch from one company to another as competing companies lure them away with even better offers. One consulting company, Markanalytics, has collected data on a sample of analysts with undergraduate degrees they hired several years ago. The data are in the file analysts. The variables are as follows:

• Starting Salary: employee’s starting salary at Markanalytics

• On Road Pct: percentage of time employee has spent on the road with clients

• State Univ: whether the employee graduated from State University (Markanalytics’s principal source of recruits)

• CIS Degree: whether the employee majored in Computer Information Systems (CIS) or a similar computer-related area

• Stayed 3 Years: whether the employee stayed at least three years with Markanalytics

• Tenure: tenure of employee at Markanalytics (months) if he or she moved before three years Markanalytics is trying to learn everything it can about retention of these valuable employees. You can help by solving the following problems and then, based on your analysis, presenting a report to Markanalytics.

1. 1.1. Although starting salaries are in a fairly narrow band, Markanalytics wonders whether they have anything to do with retention.

1.2. Find a 95% confidence interval for the mean starting salary of all employees who stay at least three years with Markanalytics. Do the same for those who leave before three years. Then find a 95% confidence interval for the difference between these means.

1.3. Among all employees whose starting salary is below the median ($37,750), find a 95% confidence interval for the proportion who stay with Markanalytics for at least three years. Do the same for the employees with starting salaries above the median. Then find a 95% confidence interval for the difference between these proportions.

1 2. Markanalytics wonders whether the percentage of time on the road might influence who stays and who leaves. Repeat the previous problem, but now do the analysis in terms of percentage of time on the road rather than starting salary. (The median percentage of time on the road is 54%.)

3. Find a 95% confidence interval for the mean tenure (in months) of all employees who leave Markanalytics within three years of being hired. Why is it not possible with the given data to find a confidence interval for the mean tenure at Markanalytics among all systems analysts hired by Markanalytics?

4. State University’s students, particularly those in its nationally acclaimed CIS area, have traditionally been among the best of Markanalytics’ recruits. But are they relatively hard to retain? Find one or more relevant confidence intervals to help you make an argument one way or the other.
 

Problem 2
Regression analysis is a method for relating one variable to other explanatory variables. However, the term regression has sometimes been used in a slightly different way, meaning “regression toward the mean.” The example often cited is of male heights. If a father is unusually tall, for example, his son will typically be taller than average but not as tall as the father. Similarly, if a father is unusually short, the son will typically be shorter than average but not as short as the father. We say that the son’s height tends to regress toward the mean. This case illustrates how regression toward the mean can occur. Suppose a company administers an aptitude test to all of its job applicants. If an applicant scores below some value, he or she cannot be hired immediately but is allowed to retake a similar exam at a later time. In the interim the applicant can presumably study to prepare for the second exam. If we focus on the applicants who fail the exam the first time and then take it a second time, we would probably expect them to score better on the second exam. One plausible reason is that they are more familiar with the exam the second time. However, we will rule this out by assuming that the two exams are sufficiently different from one another. A second plausible reason is that the applicants have studied between exams, which has a beneficial effect. However, we will argue that even if studying has no beneficial effect whatsoever, these applicants will tend to do better the second time around. The reason is regression toward the mean. All of these applicants scored unusually low on the first exam, so they will tend to regress toward the mean on the second exam—that is, they will tend to score higher. You can employ simulation to demonstrate this phenomenon, using the following model. Assume that the scores of all potential applicants are normally distributed with mean µ and standard deviation ?. Because we are assuming that any studying between exams has no beneficial effect, this distribution of scores is the same on the second exam as on the first. An applicant fails the first exam if his or her score is below some cutoff value L. Now, we would certainly expect scores on the two exams to be positively correlated, with some correlation ? . (This is the Greek letter “rho,” often used for a population correlation.) That is, if everyone took both exams, applicants who scored high on the first would tend to score high on the second, and those who scored low on the first would tend to score low on the second. (This isn’t regression to the mean, but simply that some applicants are better than others.) Given this model, you can proceed by simulating many pairs of scores, one pair for each 2 applicant. The scores for each exam should be normally distributed with parameters µ and ? but the trick is to make them correlated. You can use our Binormal function to do this. (Binormal is short for bivariate normal.) This function is supplied in the file binormal. (Binormal is not a built-in Excel function.) It takes a pair of means (both equal to µ), a pair of standard deviations (both equal to ?), and a correlation ? as arguments, with the syntax =BINORMAL (means, stdevs, correlation). To enter the formula, highlight two adjacent cells such as B5 and C5, type the formula, and press Ctrl+Shift+Enter. Then copy and paste to generate similar values for other applicants. Once you have generated pairs of scores for many applicants, you should ignore all pairs except for those where the score on the first exam is less than L. (Sorting is suggested here, but freeze the random numbers first.) For these pairs, test whether the mean score on the second exam is higher than on the first, using a paired-samples test. If it is, you have demonstrated regression toward the mean. As you will probably discover, however, the results will depend on the values of the parameters you choose for µ, ?, ?, and L. You should experiment with these. Assuming that you are able to demonstrate regression toward the mean, can you explain intuitively why it occurs?
 

Problem 3 1.
Many people believe that there is a “Friday effect” in the stock market. They don’t necessarily spell out exactly what they mean by this, but there is a sense that stock prices tend to be lower on Fridays than on other days. Because stock prices are readily available on the Web, it should be fairly easy to test this (alternative) hypothesis empirically. Before collecting data and running a test, however, you must decide exactly which hypotheses you want to test because there are several possibilities. Formulate at least two sets of null and alternative hypotheses. Then gather some stock price data and test your hypotheses. Can you conclude that there is a statistically significant Friday effect in the stock market?

2. Collect historical data from the NSE. Ten years or more should be good. Determine the probability of any stock of your choice exceeding 10% using Monte Carlo Simulation.