Calculation Questions

You can use either Excel or R to answer the assignment questions:

Question 1 The historical returns on a balanced portfolio have had an average return of 8% and a standard deviation of 12%. Assume that returns on this portfolio follow a normal distribution. What percentage of returns were greater than 20% ?

Question 2 The average rent in a city is $1,500 per month with a standard deviation of $250. Assume rent follows the normal distribution. What percentage of rents are between $1,250 and $1,750 ?

Questions 3 A popular weight loss program claims that with its recommended healthy diet regimen, users lose significant weight within a month. In order to estimate the mean weight loss of all customers, a nutritionist takes a sample of 18 dieters and records their weight loss one month after joining the program. He computes the mean and the standard deviation of weight loss as 12.5 pounds and 9.2 pounds, respectively. He believes that weight loss is likely to be normally distributed. Calculate the 95% confidence interval for the mean weight loss.

Question 4 The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. Although it requires successful completion of three levels of grueling exams, the designation often results in a promising career with a lucrative salary. A student of finance is curious about the average salary of a CFA charterholder. He takes a random sample of 36 recent charterholders and computes a mean salary of $158,000 with a standard deviation of $36,000. Use this sample information to determine the 95% confidence interval for the average salary of a CFA charterholder.

Question 5 A sample of 5,324 Americans were asked about what matters most to them in a place to live. Thirty- seven percent of the respondents felt job opportunities matter most. Construct the 90% confidence interval for the proportion of Americans who feel that good job opportunities matter most in a place to live.

Question 6 Construct the null and the alternative hypotheses for the following claims: "I am going to get the majority of the votes to win this election." "I suspect that your 10 -inch pizzas are, on average, less than 10 inches in size." "I will have to fine the company because its tablets do not contain an average of 250 mg of ibuprofen as advertised."

Question 7 This past year, home prices in the Midwest increased by an average of 6.6%. A Realtor collects data on 36 home sales in the West. He finds an average increase in home prices of 7.5%, with a standard deviation of 2%. Can he conclude that the average increase in home prices in the West is greater than the increase in the Midwest? Use a 5% significance level for the analysis.

Question 8 Some first-time home buyers-especially millennials are raiding their retirement accounts to cover the down payment on a home. An economist is concerned that the percentage of millennials who will dip into their retirement accounts to fund a home now exceeds 20%. He randomly surveys 190 millennials with retirement accounts and finds that 50 are borrowing against them. a. Set up the null and the alternative hypotheses to test the economist's concern. b. Calculate the value of the test statistic and the p-value. c. Determine if the economist's concern is justifiable at =0.05.

Short Answer Questions Please briefly answer each of the following questions: 1. What is the central limit theorem? How is the theorem applied to analytics? 2. What is the role of the sampling distribution of the same mean and proportion?