Elementary Statistics: A Step By Step Approach
10th Edition
ISBN: 9781259755330
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Chapter 7.2, Problem 6E
For Exercises 5 through 20, assume that all variables are approximately
6. Digital Camera Prices The prices (in dollars) for a particular model of digital camera with 18.0 megapixels and a f/3.5−5.6 zoom lens are shown here for 10 randomly selected online retailers. Estimate the true
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Question 2. An American option on a stock has payoff given by F = f(St) when it is exercised
at time t. We know that the function f is convex. A person claims that because of convexity,
it is optimal to exercise at expiration T. Do you agree with them?
Question 4. We consider a CRR model with So == 5 and up and down factors u = 1.03 and
d = 0.96. We consider the interest rate r = 4% (over one period). Is this a suitable CRR
model? (Explain your answer.)
Question 3. We want to price a put option with strike price K and expiration T. Two financial
advisors estimate the parameters with two different statistical methods: they obtain the same
return rate μ, the same volatility σ, but the first advisor has interest r₁ and the second advisor
has interest rate r2 (r1>r2). They both use a CRR model with the same number of periods to
price the option. Which advisor will get the larger price? (Explain your answer.)
Chapter 7 Solutions
Elementary Statistics: A Step By Step Approach
Ch. 7.1 - What is the difference between a point estimate...Ch. 7.1 - What information is necessary to calculate a...Ch. 7.1 - What is the margin of error?Ch. 7.1 - What is meant by the 95% confidence interval of...Ch. 7.1 - What are three properties of a good estimator?Ch. 7.1 - What statistic best estimates ?Ch. 7.1 - Find each. a. z/2 for the 99% confidence interval...Ch. 7.1 - What is necessary to determine the sample size?Ch. 7.1 - Fuel Efficiency of Cars and Trucks Since 1975 the...Ch. 7.1 - Fast-Food Bills for Drive-Thru Customers A random...
Ch. 7.1 - Overweight Men For a random sample of 60...Ch. 7.1 - Number of Jobs A sociologist found that in a...Ch. 7.1 - Number of Faculty The numbers of faculty at 32...Ch. 7.1 - Freshmen GPAs First-semester GPAs for a random...Ch. 7.1 - Carbohydrate Grams in Commercial Subs The number...Ch. 7.1 - Number of Farms A random sample of the number of...Ch. 7.1 - Gasoline Use A random sample of 36 drivers used on...Ch. 7.1 - Day Care Tuition A random sample of 50...Ch. 7.1 - Hospital Noise Levels Noise levels at various area...Ch. 7.1 - Length of Growing Seasons The growing seasons for...Ch. 7.1 - Christmas Presents How large a sample is needed to...Ch. 7.1 - Hospital Noise Levels In the hospital study cited...Ch. 7.1 - Internet Viewing A researcher wishes to estimate...Ch. 7.1 - Cost of Pizzas A pizza shop owner wishes to find...Ch. 7.1 - Water Temperature If the variance of the water...Ch. 7.1 - Undergraduate GPAs It is desired to estimate the...Ch. 7.2 - Sport Drink Decision Assume you get a new job as a...Ch. 7.2 - What are the properties of the t distribution?Ch. 7.2 - What is meant by degrees of freedom?Ch. 7.2 - Find the values for each. a. t/2 and n = 18 for...Ch. 7.2 - When should the t distribution be used to find a...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - For Exercises 5 through 20, assume that all...Ch. 7.2 - Parking Meter Revenue A one-sided confidence...Ch. 7.3 - Contracting Influenza To answer the questions, use...Ch. 7.3 - In each case, find p and q. a. n = 80 and X = 40...Ch. 7.3 - Find p and q for each situation. a. n = 60 and X =...Ch. 7.3 - Cyber Monday Shopping A survey of 1000 U.S. adults...Ch. 7.3 - Manual Transmission Automobiles In 2014, six...Ch. 7.3 - Holiday Gifts A survey of 100 Americans found that...Ch. 7.3 - Belief in Haunted Places A random sample of 205...Ch. 7.3 - Work Interruptions Research by Steelcase found the...Ch. 7.3 - Travel to Outer Space A CBS News/New York Times...Ch. 7.3 - High School Graduates Who Take the SAT The...Ch. 7.3 - Educational Television In a random sample of 200...Ch. 7.3 - Wi-Fi Access A survey of 50 students in grades 4...Ch. 7.3 - Students Who Major in Business It has been...Ch. 7.3 - Smartphone Ownership A recent survey of 349 people...Ch. 7.3 - Home Internet Access According to a study, 96% of...Ch. 7.3 - Overseas Travel A researcher wishes to be 95%...Ch. 7.3 - Widows A recent study indicated that 29% of the...Ch. 7.3 - Direct Satellite Television It is believed that...Ch. 7.3 - Obesity Obesity is defined as a body mass index...Ch. 7.3 - U.S. Fitness Guidelines According to the World...Ch. 7.3 - Diet Habits A federal report indicated that 27% of...Ch. 7.3 - Gun Control If a random sample of 600 people is...Ch. 7.3 - Survey on Politics In a study, 68% of 1015...Ch. 7.4 - Ages of Presidents at the Time of Their Deaths...Ch. 7.4 - What distribution must be used when computing...Ch. 7.4 - What assumption must be made when computing...Ch. 7.4 - Using Table G, find the values for 2 left and 2...Ch. 7.4 - Lifetimes of Wristwatches Find the 90% confidence...Ch. 7.4 - Carbohydrates in Yogurt The number of...Ch. 7.4 - Carbon Monoxide Deaths A study of...Ch. 7.4 - Pacemaker Batteries A manufacturer of pacemakers...Ch. 7.4 - Age of College Students Find the 90% confidence...Ch. 7.4 - Prob. 9ECh. 7.4 - Stock Prices A random sample of stock prices per...Ch. 7.4 - Cost of an Operation A medical researcher surveyed...Ch. 7.4 - Home Ownership Rates The percentage rates of home...Ch. 7.4 - Calories in a Standard Size Candy Bar Estimate the...Ch. 7.4 - SAT Scores Estimate the variance in mean...Ch. 7.4 - Daily Cholesterol Intake The American Heart...Ch. 7.4 - Calculator Battery Lifetimes A confidence interval...Ch. 7 - Eye Blinks A survey of 49 individuals found that...Ch. 7 - Vacation Days A U.S. Travel Data Center survey...Ch. 7 - Blood Pressure A researcher wishes to estimate...Ch. 7 - Shopping Survey A random sample of 49 shoppers...Ch. 7 - Lengths of Childrens Animated Films The lengths...Ch. 7 - Dog Bites to Postal Workers For a certain urban...Ch. 7 - Number of Credit Cards In a recent survey of 1000...Ch. 7 - Vacation Sites A U.S. Travel Data Centers survey...Ch. 7 - Prob. 7.3.9RECh. 7 - Adult Educational Activities A local county has a...Ch. 7 - Prob. 7.3.11RECh. 7 - Child Care Programs A study found that 73% of...Ch. 7 - Baseball Diameters The standard deviation of the...Ch. 7 - Cost of an Operation A medical researcher surveyed...Ch. 7 - Lifetimes of Snowmobiles A random sample of 15...Ch. 7 - Length of Childrens Animated Films Use the data...Ch. 7 - From the Data Bank choose a variable, find the...Ch. 7 - Repeat Exercise 1, using a different variable and...Ch. 7 - Repeat Exercise 1, using a proportion. For...Ch. 7 - From Data Set III in Appendix B, select a sample...Ch. 7 - From Data Set VI in Appendix B, select a sample of...Ch. 7 - Select a random sample of 20 of the record high...Ch. 7 - Determine whether each statement is true or false....Ch. 7 - Determine whether each statement is true or false....Ch. 7 - Determine whether each statement is true or false....Ch. 7 - Determine whether each statement is true or false....Ch. 7 - When a 99% confidence interval is calculated...Ch. 7 - The best point estimate of the population mean is...Ch. 7 - When the population standard deviation is unknown...Ch. 7 - Complete the following statements with the best...Ch. 7 - Complete the following statements with the best...Ch. 7 - Complete the following statements with the best...Ch. 7 - Complete the following statements with the best...Ch. 7 - Cost of Texts An irate student complained that the...Ch. 7 - Doctor Visit Costs An irate patient complained...Ch. 7 - Weights of Minivans The average weight of 40...Ch. 7 - Ages of Insurance Representatives In a study of 10...Ch. 7 - Prob. 16CQCh. 7 - Burglaries For a certain urban area, it was found...Ch. 7 - Hours Spent Studying A university dean wishes to...Ch. 7 - Prob. 19CQCh. 7 - Prob. 20CQCh. 7 - Prob. 21CQCh. 7 - Prob. 22CQCh. 7 - Prob. 23CQCh. 7 - Prob. 24CQCh. 7 - Prob. 25CQCh. 7 - Prob. 26CQCh. 7 - Critical Thinking Challenges A confidence interval...
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- We consider an N-period CRR model where each period is 1 year (At = 1), the up factor is u = 0.1, the down factor is d = e−0.3 and r = 0. We remind you that in the CRR model, the stock price at time tn is modeled (under P) by Sta = So exp (μtn + σ√AtZn), where (Zn) is a simple symmetric random walk. (a) Find the parameters μ and σ for the CRR model described above. (b) Find P Ste So 55/50 € > 1). StN (c) Find lim P 804-N (d) Determine q. (You can use e- 1 x.) Ste (e) Find Q So (f) Find lim Q 004-N StN Soarrow_forwardIn this problem, we consider a 3-period stock market model with evolution given in Fig. 1 below. Each period corresponds to one year. The interest rate is r = 0%. 16 22 28 12 16 12 8 4 2 time Figure 1: Stock evolution for Problem 1. (a) A colleague notices that in the model above, a movement up-down leads to the same value as a movement down-up. He concludes that the model is a CRR model. Is your colleague correct? (Explain your answer.) (b) We consider a European put with strike price K = 10 and expiration T = 3 years. Find the price of this option at time 0. Provide the replicating portfolio for the first period. (c) In addition to the call above, we also consider a European call with strike price K = 10 and expiration T = 3 years. Which one has the highest price? (It is not necessary to provide the price of the call.) (d) We now assume a yearly interest rate r = 25%. We consider a Bermudan put option with strike price K = 10. It works like a standard put, but you can exercise it…arrow_forwardIn this problem, we consider a 2-period stock market model with evolution given in Fig. 1 below. Each period corresponds to one year (At = 1). The yearly interest rate is r = 1/3 = 33%. This model is a CRR model. 25 15 9 10 6 4 time Figure 1: Stock evolution for Problem 1. (a) Find the values of up and down factors u and d, and the risk-neutral probability q. (b) We consider a European put with strike price K the price of this option at time 0. == 16 and expiration T = 2 years. Find (c) Provide the number of shares of stock that the replicating portfolio contains at each pos- sible position. (d) You find this option available on the market for $2. What do you do? (Short answer.) (e) We consider an American put with strike price K = 16 and expiration T = 2 years. Find the price of this option at time 0 and describe the optimal exercising strategy. (f) We consider an American call with strike price K ○ = 16 and expiration T = 2 years. Find the price of this option at time 0 and describe…arrow_forward
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