Stats
5th Edition
ISBN: 9780135163825
Author: De Veaux, Richard D., Velleman, Paul F., BOCK, David E.
Publisher: Pearson,
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Chapter 18, Problem 8E
a.
To determine
State the null and alternative hypothesis.
b.
To determine
State the model and requirements of the hypothesis test.
c.
To determine
Calculate the test statistic and P-value.
d.
To determine
State the conclusion.
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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 18 Solutions
Stats
Ch. 18.2 - 1. A research team wants to know if aspirin helps...Ch. 18.2 - 2. An allergy drug has been tested and found to...Ch. 18.2 - 3. The new drug is tested and the P-value is...Ch. 18.4 - 4. The research team that wants to know if aspirin...Ch. 18.4 - 5. A marketing team wants to test whether their...Ch. 18.6 - 6. A bank is testing a new method for getting...Ch. 18.6 - Prob. 7JCCh. 18.6 - Prob. 8JCCh. 18 - Prob. 1ECh. 18 - Prob. 2E
Ch. 18 - Prob. 3ECh. 18 - 4. Hypotheses and parameters As in Exercise 3, for...Ch. 18 - Prob. 5ECh. 18 - 6. GRE performance A test preparation company...Ch. 18 - Prob. 7ECh. 18 - Prob. 8ECh. 18 - Prob. 9ECh. 18 - 10. Marriage In 1960, census results indicated...Ch. 18 - Prob. 11ECh. 18 - Prob. 12ECh. 18 - Prob. 13ECh. 18 - Prob. 14ECh. 18 - Prob. 15ECh. 18 - 16. More hypotheses Write the null and alternative...Ch. 18 - Prob. 17ECh. 18 - Prob. 18ECh. 18 - Prob. 19ECh. 18 - 20. Cars A survey investigating whether the...Ch. 18 - Prob. 21ECh. 18 - Prob. 22ECh. 18 - Prob. 23ECh. 18 - Prob. 24ECh. 18 - Prob. 25ECh. 18 - Prob. 26ECh. 18 - Prob. 27ECh. 18 - 28. Educated mothers The National Center for...Ch. 18 - Prob. 29ECh. 18 - Take the offer II We saw in Chapter 16, Exercise...Ch. 18 - Prob. 31ECh. 18 - Prob. 32ECh. 18 - Prob. 33ECh. 18 - 34. Football 2016 During the first 15 weeks of the...Ch. 18 - Prob. 35ECh. 18 - Prob. 36ECh. 18 - Prob. 37ECh. 18 - 38. Jury Census data for a certain county show...Ch. 18 - Prob. 39ECh. 18 - Prob. 40ECh. 18 - Prob. 41ECh. 18 - Prob. 42ECh. 18 - 43. John Wayne Like a lot of other Americans, John...Ch. 18 - Prob. 44ECh. 18 - Prob. 45ECh. 18 - 46. Hot dogs again The nutrition lab in Chapter...Ch. 18 - Prob. 47ECh. 18 - 48. Computer lab fees again The technology...Ch. 18 - Prob. 49ECh. 18 - Prob. 50ECh. 18 - Prob. 51ECh. 18 - More ski wax From Chapter 17, Exercise 58, Bjork...Ch. 18 - Prob. 53ECh. 18 - Prob. 54ECh. 18 - Prob. 55ECh. 18 - Prob. 56ECh. 18 - Prob. 57ECh. 18 - Prob. 58ECh. 18 - Prob. 59ECh. 18 - 60. BMI According to the Centers for Disease...
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- 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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