Introductory Statistics
3rd Edition
ISBN: 9780135188927
Author: Gould, Robert, Ryan, Colleen N. (colleen Nooter)
Publisher: Pearson,
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Chapter 9, Problem 19SE
To determine
Find the "
a .
To determine
Identify the correct interpretation for the confidence interval among the three given options.
b .
To determine
Explain whether it can be believed that the population mean GPA is 3.80 based on the confidence interval.
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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 9 Solutions
Introductory Statistics
Ch. 9 - Ages A study of all the students at a small...Ch. 9 - Units A survey of 100 random full-time students at...Ch. 9 - Exam Scores The distribution of the scores on a...Ch. 9 - Exam Scores The distribution of the scores on a...Ch. 9 - Showers According to home-water-works.org, the...Ch. 9 - Smartphones According to a 2017 report by ComScore...Ch. 9 - Retirement Income Several times during the year,...Ch. 9 - Time Employed A human resources manager for a...Ch. 9 - Driving (Example 1) Drivers in Wyoming drive more...Ch. 9 - Driving Drivers in Alaska drive fewer miles yearly...
Ch. 9 - Babies Weights (Example 2) Some sources report...Ch. 9 - Babies’ Weights, Again Some sources report that...Ch. 9 - (Example 3) Income in Maryland According to a 2018...Ch. 9 - Income in Kansas According to a 2018 Money...Ch. 9 - CLT Shapes (Example 4) One of the histograms is a...Ch. 9 - Used Van Costs One histogram shows the...Ch. 9 - (Example 5) Age of Used Vans The mean age of all...Ch. 9 - Student Ages The mean age of all 2550 students at...Ch. 9 - Prob. 19SECh. 9 - Prob. 20SECh. 9 - Prob. 21SECh. 9 - Prob. 22SECh. 9 - Private University Tuition (Example 7) A random...Ch. 9 - Random Numbers If you take samples of 40 lines...Ch. 9 - t* (Example 8) A researcher collects one sample of...Ch. 9 - t* A researcher collects a sample of 25...Ch. 9 - Heights of 12th Graders (Example 9) A random...Ch. 9 - Drinks A fast-food chain sells drinks that it...Ch. 9 - Men’s Pulse Rates (Example 10) A random sample of...Ch. 9 - Travel Time to School A random sample of 50...Ch. 9 - RBIs (Example 11) A random sample of 25 baseball...Ch. 9 - RBIs Again In exercise 9.31, two intervals were...Ch. 9 - Confidence Interval Changes State whether each of...Ch. 9 - Confidence Interval Changes State whether each of...Ch. 9 - Potatoes The weights of four randomly and...Ch. 9 - Tomatoes The weights of four randomly and...Ch. 9 - Human Body Temperatures (Example 12) A random...Ch. 9 - Reaction Distance Data on the disk and website...Ch. 9 - Potatoes Use the data from exercise 9.35. a. If...Ch. 9 - Tomatoes Use the data from exercise 9.36. a. Using...Ch. 9 - Cholesterol In the U.S. Department of Health has...Ch. 9 - BMI A body mass index (BMI) of more than 25 is...Ch. 9 - Male Height In the United States, the population...Ch. 9 - Female Height In the United States, the population...Ch. 9 - Deflated Footballs? Patriots In the 2015 AFC...Ch. 9 - Deflated Footballs? Colts In the 2015 AFC...Ch. 9 - Movie Ticket Prices According to Deadline.com, the...Ch. 9 - Broadway Ticket Prices According to Statista.com,...Ch. 9 - Atkins Diet Difference Ten people went on an...Ch. 9 - Pulse Difference The following numbers are the...Ch. 9 - Student Ages Suppose that 200 statistics students...Ch. 9 - Presidents’ Ages at Inauguration A 95 confidence...Ch. 9 - Independent or Paired (Example 13) State whether...Ch. 9 - Independent or Paired State whether each situation...Ch. 9 - Televisions: CI (Example 14) Minitab output is...Ch. 9 - Pulse and Gender: CI Using data from NHANES, we...Ch. 9 - Televisions (Example 15) The table shows the...Ch. 9 - Pulse Rates Using data from NHANES, we looked at...Ch. 9 - Triglycerides Triglycerides are a form of fat...Ch. 9 - Systolic Blood Pressures When you have your blood...Ch. 9 - Triglycerides, Again Report and interpret the 95...Ch. 9 - Blood Pressures, Again Report and interpret the 95...Ch. 9 - Baseball Salaries A random sample of 40...Ch. 9 - College Athletes’ Weights A random sample of male...Ch. 9 - Baseball Salaries In exercise 9.63 you could not...Ch. 9 - College Athletes’ Weights In exercise 9.64, you...Ch. 9 - Textbook Prices, UCSB vs. CSUN (Example 16) The...Ch. 9 - Textbook Prices. OC vs. CSUN The prices of a...Ch. 9 - Females’ Pulse Rates before and after a Fright...Ch. 9 - Males’ Pulse Rates before and after a Fright...Ch. 9 - Organic Food A student compared organic food...Ch. 9 - Body Temperature The body temperatures of 65 men...Ch. 9 - Ales vs. IPAs Data were collected on calorie...Ch. 9 - Surfers Surfers and statistics students Rex...Ch. 9 - Self-Reported Heights of Men (Example 18) A random...Ch. 9 - Eating Out Jacqueline Loya, a statistics student,...Ch. 9 - Prob. 77SECh. 9 - Self-Driving Cars A survey of asked respondents...Ch. 9 - Women’s Heights Assume women’s heights are...Ch. 9 - Showers According to home-water-works.org, the...Ch. 9 - Choose a test for each situation: one-sample...Ch. 9 - Choose a t-test for each situation: one-sample...Ch. 9 - Cones: 3 Tests A McDonald’s fact sheet says its...Ch. 9 - Prob. 84CRECh. 9 - Brain Size Brain size for 20 random women and 20...Ch. 9 - Reducing Pollution A random sample of 12th-grade...Ch. 9 - Heart Rate before and after Coffee Elena Lucin, a...Ch. 9 - Exam Grades The final exam grades for a sample of...Ch. 9 - Hours of Television Viewing The number of hours...Ch. 9 - Reaction Distances Reaction distances in...Ch. 9 - Ales vs. Lagers Data were collected on calorie...Ch. 9 - Weights of Hockey and Baseball Players Data were...Ch. 9 - Grocery Delivery The table shows the prices for...Ch. 9 - Parents The following table shows the heights (in...Ch. 9 - Why Is n1 in the Sample Standard Deviation? Why do...Ch. 9 - Prob. 96CRECh. 9 - Construct two sets of body temperatures (in...Ch. 9 - Construct heights for 3 or more sets of twins (6...
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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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