Applied Statistics in Business and Economics
5th Edition
ISBN: 9780077837303
Author: David Doane, Lori Seward Senior Instructor of Operations Management
Publisher: McGraw-Hill Education
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Chapter 9, Problem 10CR
a.
To determine
In a hypothesis test for a proportion, when normality can be assumed.
b.
To determine
Describe the distribution if the
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We consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…
Negate the following compound statement using De Morgans's laws.
Chapter 9 Solutions
Applied Statistics in Business and Economics
Ch. 9.2 - If you repealed a hypothesis test 1,000 times (in...Ch. 9.2 - Define Type I and Type II errors for each...Ch. 9.2 - A firm decides to test its employees for illegal...Ch. 9.2 - A hotel installs smoke detectors with adjustable...Ch. 9.2 - What is the consequence of a false negative in an...Ch. 9.2 - Prob. 6SECh. 9.3 - A manufacturer claims that its compact fluorescent...Ch. 9.3 - Prob. 8SECh. 9.3 - Prob. 9SECh. 9.3 - The average age of a part-time seasonal employee...
Ch. 9.3 - Prob. 11SECh. 9.3 - Prob. 12SECh. 9.4 - Find the zcalc test statistic for each hypothesis...Ch. 9.4 - Prob. 14SECh. 9.4 - Prob. 15SECh. 9.4 - Prob. 16SECh. 9.4 - Green Beam Ltd. claims that its compact...Ch. 9.4 - The mean potassium content of a popular sports...Ch. 9.4 - Calculate the test statistic and p-value for each...Ch. 9.4 - Determine the p-value for each test statistic. a....Ch. 9.4 - Procyon Mfg. produces tennis balls. Weights are...Ch. 9.4 - The mean arrival rate of flights at OHare Airport...Ch. 9.4 - Prob. 23SECh. 9.4 - The Scottsdale fire department aims to respond to...Ch. 9.4 - The lifespan of xenon metal halide arc-discharge...Ch. 9.4 - Discuss the issues of statistical significance and...Ch. 9.4 - The target activation force of the buttons on a...Ch. 9.5 - Find the tcalc test statistic for each hypothesis...Ch. 9.5 - Find the critical value of Students t for each...Ch. 9.5 - Find the critical value of Students t for each...Ch. 9.5 - Find the tcalc test statistic for each hypothesis...Ch. 9.5 - Estimate the p-value as a range using Appendix D...Ch. 9.5 - Prob. 33SECh. 9.5 - Prob. 34SECh. 9.5 - Prob. 35SECh. 9.5 - The manufacturer of an airport baggage scanning...Ch. 9.5 - Prob. 37SECh. 9.5 - The average weight of a package of rolled oats is...Ch. 9.5 - According to J.D. Power & Associates, the mean...Ch. 9.5 - Prob. 40SECh. 9.5 - Prob. 41SECh. 9.5 - Prob. 42SECh. 9.5 - Prob. 43SECh. 9.6 - Interpret each p-value in your own words: a....Ch. 9.6 - Prob. 45SECh. 9.6 - Prob. 46SECh. 9.6 - May normality of the sample proportion p be...Ch. 9.6 - Prob. 48SECh. 9.6 - In a hospitals shipment of 3,500 insulin syringes,...Ch. 9.6 - Prob. 50SECh. 9.6 - Prob. 51SECh. 9.6 - The recent default rate on all student loans is...Ch. 9.6 - Prob. 53SECh. 9.6 - Prob. 54SECh. 9.6 - BriteScreen, a manufacturer of 19-inch LCD...Ch. 9.6 - Perfect pitch is the ability to identify musical...Ch. 9.7 - A quality expert insects 400 items to test whether...Ch. 9.7 - Prob. 58SECh. 9.7 - For a certain wine, the mean pH (a measure of...Ch. 9.7 - Repeat the previous exercise, using = .05. For...Ch. 9.8 - A sample of size n = 15 has variance s2 = .35. At ...Ch. 9.8 - Prob. 62SECh. 9.8 - A sample of size n = 19 has variance s2 = .1.96....Ch. 9.8 - Prob. 64SECh. 9.8 - Prob. 65SECh. 9 - (a) List the steps in testing a hypothesis, (b)...Ch. 9 - (a) Explain the difference between the null...Ch. 9 - (a) Why do we say fail to reject H0 instead of...Ch. 9 - (a) Define Type I error and Type II error. (b)...Ch. 9 - (a) Explain the difference between a left-tailed...Ch. 9 - Prob. 6CRCh. 9 - Prob. 7CRCh. 9 - (a) Why do we prefer low values for and ? (b) For...Ch. 9 - Prob. 10CRCh. 9 - Prob. 11CRCh. 9 - (a) Explain what a p-value means. Give an example...Ch. 9 - Prob. 13CRCh. 9 - (a) What does a power curve show? (b) What factors...Ch. 9 - (a) In testing a hypothesis about a variance, what...Ch. 9 - Suppose you always reject the null hypothesis,...Ch. 9 - Suppose the judge decides to acquit all...Ch. 9 - High blood pressure, if untreated, can lead to...Ch. 9 - A nuclear power plant replaces its ID card...Ch. 9 - A test-preparation company advertises that its...Ch. 9 - Prob. 71CECh. 9 - Prob. 72CECh. 9 - Prob. 73CECh. 9 - Pap smears are a test for abnormal cancerous and...Ch. 9 - Prob. 75CECh. 9 - Prob. 76CECh. 9 - Malcheon Health Clinic claims that the average...Ch. 9 - The sodium content of a popular sports drink is...Ch. 9 - A can of peeled whole tomatoes is supposed to...Ch. 9 - At Ajax Spring Water, a half-liter bottle of soft...Ch. 9 - Prob. 81CECh. 9 - Prob. 82CECh. 9 - A U.S. dime weighs 2.268 grams when minted. A...Ch. 9 - A coin was flipped 60 times and came up heads 38...Ch. 9 - Prob. 85CECh. 9 - Prob. 86CECh. 9 - Prob. 87CECh. 9 - Prob. 88CECh. 9 - Prob. 89CECh. 9 - Prob. 90CECh. 9 - Prob. 91CECh. 9 - Prob. 92CECh. 9 - The average service time at a Noodles Company...Ch. 9 - Prob. 94CECh. 9 - Prob. 95CECh. 9 - Beer shelf life is a problem for brewers and...Ch. 9 - Prob. 97CECh. 9 - Prob. 99CECh. 9 - Prob. 100CECh. 9 - Prob. 101CECh. 9 - Prob. 102CECh. 9 - An experimental medication is administered to 16...Ch. 9 - The historical on-time percentage for Amtraks...Ch. 9 - After 7 months, none of 238 angioplasty patients...Ch. 9 - A certain brand of flat white interior latex paint...Ch. 9 - Prob. 107CECh. 9 - Prob. 108CECh. 9 - Prob. 109CE
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- Negate the following compound statement using De Morgans's laws.arrow_forwardQuestion 6: Negate the following compound statements, using De Morgan's laws. A) If Alberta was under water entirely then there should be no fossil of mammals.arrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forward
- Characterize (with proof) all connected graphs that contain no even cycles in terms oftheir blocks.arrow_forwardLet G be a connected graph that does not have P4 or C3 as an induced subgraph (i.e.,G is P4, C3 free). Prove that G is a complete bipartite grapharrow_forwardProve sufficiency of the condition for a graph to be bipartite that is, prove that if G hasno odd cycles then G is bipartite as follows:Assume that the statement is false and that G is an edge minimal counterexample. That is, Gsatisfies the conditions and is not bipartite but G − e is bipartite for any edge e. (Note thatthis is essentially induction, just using different terminology.) What does minimality say aboutconnectivity of G? Can G − e be disconnected? Explain why if there is an edge between twovertices in the same part of a bipartition of G − e then there is an odd cyclearrow_forward
- Let G be a connected graph that does not have P4 or C4 as an induced subgraph (i.e.,G is P4, C4 free). Prove that G has a vertex adjacent to all othersarrow_forwardWe consider a one-period market with the following properties: the current stock priceis S0 = 4. At time T = 1 year, the stock has either moved up to S1 = 8 (with probability0.7) or down towards S1 = 2 (with probability 0.3). We consider a call option on thisstock with maturity T = 1 and strike price K = 5. The interest rate on the money marketis 25% yearly.(a) Find the replicating portfolio (φ, ψ) corresponding to this call option.(b) Find the risk-neutral (no-arbitrage) price of this call option.(c) We now consider a put option with maturity T = 1 and strike price K = 3 onthe same market. Find the risk-neutral price of this put option. Reminder: A putoption gives you the right to sell the stock for the strike price K.1(d) An investor with initial capital X0 = 0 wants to invest on this market. He buysα shares of the stock (or sells them if α is negative) and buys β call options (orsells them is β is negative). He invests the cash balance on the money market (orborrows if the amount is…arrow_forwardDetermine if the two statements are equivalent using a truth tablearrow_forward
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