Intro Stats
4th Edition
ISBN: 9780321825278
Author: Richard D. De Veaux, Paul F. Velleman, David E. Bock
Publisher: PEARSON
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Chapter 10, Problem 14E
Student center survey For their class project, a group of statistics students decide to survey the student body to assess opinions about the proposed new student center. Their sample of 200 contained 50 first-year students, 50 sophomores, 50 juniors, and 50 seniors.
- a) Do you think the group was using an SRS? Why?
- b) What sampling design do you think they used?
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Students have asked these similar questions
T1.4: Let ẞ(G) be the minimum size of a vertex cover, a(G) be the maximum size of an
independent set and m(G) = |E(G)|.
(i) Prove that if G is triangle free (no induced K3) then m(G) ≤ a(G)B(G). Hints - The
neighborhood of a vertex in a triangle free graph must be independent; all edges have at least
one end in a vertex cover.
(ii) Show that all graphs of order n ≥ 3 and size m> [n2/4] contain a triangle. Hints - you
may need to use either elementary calculus or the arithmetic-geometric mean inequality.
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 10 Solutions
Intro Stats
Ch. 10.2 - Various claims are often made for surveys. Why is...Ch. 10.4 - We need to survey a random sample of the 300...Ch. 10 - Texas AM Administrators at Texas AM University...Ch. 10 - Satisfied workers The managers of a large company...Ch. 10 - AM again The president of the university plans a...Ch. 10 - Satisfied respondents The companys annual report...Ch. 10 - Sampling students A professor teaching a large...Ch. 10 - Sampling satisfaction A company hoping to assess...Ch. 10 - Sampling AM students For each scenario, identify...Ch. 10 - Satisfactory satisfaction samples For each...
Ch. 10 - Survey students What problems do you see with...Ch. 10 - Happy employees The company plans to have the head...Ch. 10 - Student samples The university administration of...Ch. 10 - Surveying employees The company of Exercise 2 is...Ch. 10 - Roper Through their Roper Reports Worldwide, GfK...Ch. 10 - Student center survey For their class project, a...Ch. 10 - Drug tests Major League Baseball tests players to...Ch. 10 - Prob. 16ECh. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - Prob. 18ECh. 10 - Prob. 19ECh. 10 - Prob. 20ECh. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - Mistaken poll A local TV station conducted a...Ch. 10 - Another mistaken poll Prior to the mayoral...Ch. 10 - Parent opinion, part 1 In a large city school...Ch. 10 - Parent opinion, part 2 Lets revisit the school...Ch. 10 - Prob. 28ECh. 10 - Prob. 29ECh. 10 - Roller coasters An amusement park has opened a new...Ch. 10 - Playground, act two The survey described in...Ch. 10 - Wording the survey Two members of the PTA...Ch. 10 - Banning ephedra An online poll on a website asked:...Ch. 10 - Survey questions Examine each of the following...Ch. 10 - More survey questions Examine each of the...Ch. 10 - Phone surveys Any time we conduct a survey, we...Ch. 10 - Cell phone survey What about drawing a random...Ch. 10 - Fuel economy Occasionally, when I fill my car with...Ch. 10 - Prob. 40ECh. 10 - Prob. 41ECh. 10 - Quality control Sammys Salsa, a small local...Ch. 10 - A fish story Concerned about reports of discolored...Ch. 10 - Prob. 44ECh. 10 - More sampling methods Consider each of these...
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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
- Question 4: Determine if pair of statements A and B are equivalent or not, using truth table. A. (~qp)^~q в. р л~9arrow_forwardDetermine if the two statements are equalivalent using a truth tablearrow_forwardQuestion 3: p and q represent the following simple statements. p: Calgary is the capital of Alberta. A) Determine the value of each simple statement p and q. B) Then, without truth table, determine the va q: Alberta is a province of Canada. for each following compound statement below. pvq р^~q ~рл~q ~q→ p ~P~q Pq b~ (d~ ← b~) d~ (b~ v d) 0 4arrow_forward
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