Statistics: The Art and Science of Learning from Data (4th Edition)
4th Edition
ISBN: 9780321997838
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
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Chapter 4, Problem 61CP
To determine
Mention a lurking variable that could bias the results of such an online survey, and explain how it could affect the results.
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You have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below. please do it step by step
Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship.
Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size).
Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple linear…
Exercises: Find all the whole number
solutions of the congruence equation.
1. 3x 8 mod 11
2. 2x+3= 8 mod 12
3. 3x+12= 7 mod 10
4. 4x+6= 5 mod 8
5. 5x+3= 8 mod 12
Scenario
Sales of products by color follow a peculiar, but predictable, pattern that determines how many units will sell in
any given year. This pattern is shown below
Product Color
1995
1996
1997
Red
28
42
21
1998
23
1999
29
2000
2001
2002
Unit Sales
2003 2004
15
8
4
2
1
2005 2006
discontinued
Green
26
39
20
22
28
14
7
4
2
White
43
65
33
36
45
23
12
Brown
58
87
44
48
60
Yellow
37
56
28
31
Black
28
42
21
Orange
19
29
Purple
Total
28
42
21
49
68
78
95
123
176
181
164
127
24
179
Questions
A) Which color will sell the most units in 2007?
B) Which color will sell the most units combined in the 2007 to 2009 period?
Please show all your analysis, leave formulas in cells, and specify any assumptions you make.
Chapter 4 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Ch. 4.1 - Cell phones Consider the cell phone Study 3...Ch. 4.1 - High blood pressure and binge drinking Many...Ch. 4.1 - Low-fat versus low-carb diet? One hundred...Ch. 4.1 - Experiments versus observational studies When...Ch. 4.1 - School testing for drugs Example 3 discussed a...Ch. 4.1 - Hormone therapy and heart disease Since 1976 the...Ch. 4.1 - Speaking foreign languages A 2014 study...Ch. 4.1 - Breast-cancer screening A study published in 2010...Ch. 4.1 - Experiment or observe? Explain whether an...Ch. 4.1 - Baseball under a full moon During a baseball game...
Ch. 4.1 - Seat belt anecdote Andy once heard about a car...Ch. 4.1 - Poker as a profession? Tonys mother is extremely...Ch. 4.1 - Whats more to blame for obesity? In a study...Ch. 4.1 - Census every 10 years? A nationwide census is...Ch. 4.2 - Choosing officers A campus club consists of five...Ch. 4.2 - Simple random sample of students In Example 4, a...Ch. 4.2 - Auditing accountsapp Use an app or computer...Ch. 4.2 - Sampling from a directory A local telephone...Ch. 4.2 - Bias due to perceived race A political scientist...Ch. 4.2 - Confederates Some southern states in the United...Ch. 4.2 - Instructor ratings The website...Ch. 4.2 - Job trends The 20132014 Recruiting Trends report,...Ch. 4.2 - Gun control More than 75% of Americans answer yes...Ch. 4.2 - Violent video games and family closeness A recent...Ch. 4.2 - Fracking The journal Energy Policy (2014, 65:...Ch. 4.2 - Teens buying alcohol over Internet In August 2006,...Ch. 4.2 - Cheating spouses and bias In a survey conducted by...Ch. 4.2 - Online dating A story titled Personals, Sex Sites...Ch. 4.2 - Identify the bias A newspaper designs a survey to...Ch. 4.2 - Types of bias Give an example of a survey that...Ch. 4.3 - Smoking affects lung cancer? You would like to...Ch. 4.3 - Never leave home without duct tape There have been...Ch. 4.3 - More duct tape In a follow-up study, 103 patients...Ch. 4.3 - Vitamin B A New York Times article (March 13,...Ch. 4.3 - Facebook study During the one-week period of...Ch. 4.3 - Science faculty selection of grad students In an...Ch. 4.3 - Pain reduction medication Consider an experiment...Ch. 4.3 - Pain reduction medication, continued Consider the...Ch. 4.3 - Pain reduction medication, yet again Revisit the...Ch. 4.3 - Colds and vitamin C For some time there has been...Ch. 4.3 - Reducing high blood pressure A pharmaceutical...Ch. 4.4 - Student loan debt A researcher wants to compare...Ch. 4.4 - Club officers again In Exercise 4.15, two officers...Ch. 4.4 - Security awareness training Of 400 employees at a...Ch. 4.4 - Prob. 45PBCh. 4.4 - Prob. 46PBCh. 4.4 - Prob. 47PBCh. 4.4 - Prob. 48PBCh. 4.4 - Prob. 49PBCh. 4.4 - Prob. 50PBCh. 4.4 - Prob. 51PBCh. 4.4 - Prob. 52PBCh. 4.4 - Effect of partner smoking in smoking cessation...Ch. 4 - Cell phones If you want to conduct a study with...Ch. 4 - Observational versus experimental study Without...Ch. 4 - Unethical experimentation Give an example of a...Ch. 4 - Spinal fluid proteins and Alzheimers A research...Ch. 4 - Fear of asbestos Your friend reads about a study...Ch. 4 - NCAA mens basketball poll The last four teams of...Ch. 4 - Sampling your fellow students You are assigned to...Ch. 4 - Prob. 61CPCh. 4 - Comparing female and male students You plan to...Ch. 4 - Football discipline A large southern university...Ch. 4 - Prob. 64CPCh. 4 - Voluntary sports polls In 2014, the Pittsburgh...Ch. 4 - Video games mindless? Playing video games not so...Ch. 4 - Physicians health study Read about the first...Ch. 4 - Aspirin prevents heart attacks? During the 1980s...Ch. 4 - Prob. 69CPCh. 4 - Prob. 70CPCh. 4 - Prob. 71CPCh. 4 - Bupropion and nicotine patch study results The...Ch. 4 - Prefer Coke or Pepsi? You want to conduct an...Ch. 4 - Prob. 74CPCh. 4 - Samples not equally likely in a cluster sample? In...Ch. 4 - Nursing homes You plan to sample residents of...Ch. 4 - Multistage health survey A researcher wants to...Ch. 4 - Hazing Hazing within college fraternities is a...Ch. 4 - Prob. 79CPCh. 4 - Twins and breast cancer Excessive cumulative...Ch. 4 - Judging sampling design In each of the following...Ch. 4 - Prob. 87CPCh. 4 - Age for legal alcohol You want to investigate the...Ch. 4 - Prob. 89CPCh. 4 - Prob. 90CPCh. 4 - Issues in clinical trials A randomized clinical...Ch. 4 - Prob. 92CPCh. 4 - Prob. 93CPCh. 4 - Prob. 94CPCh. 4 - Prob. 95CPCh. 4 - Prob. 96CPCh. 4 - For Exercises 4.974.103, select the best response....Ch. 4 - Prob. 98CPCh. 4 - For Exercises 4.974.103, select the best response....Ch. 4 - For Exercises 4.974.103, select the best response....Ch. 4 - Prob. 101CPCh. 4 - For Exercises 4.974.103, select the best response....Ch. 4 - Prob. 103CPCh. 4 - Systematic sampling A researcher wants to select...Ch. 4 - Prob. 106CPCh. 4 - Prob. 107CP
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- One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs \[36\] \[20\] \[56\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] problem 1 Find the probability that a randomly selected student prefers dogs.Enter your answer as a fraction or decimal. \[P\left(\text{prefers dogs}\right)=\] Incorrect Check Hide explanation Preference Male Female TOTAL Prefers dogs \[\blueD{36}\] \[\blueD{20}\] \[\blueE{56}\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] There were \[\blueE{56}\] students in the sample who preferred dogs out of \[100\] total students.arrow_forwardBusiness discussarrow_forwardYou have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below. Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship. Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size). Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple linear regression model. Interpret the…arrow_forward
- Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. How to take snapshots: if you use a MacBook, press Command+ Shift+4 to take snapshots. If you are using Windows, use the Snipping Tool to take snapshots. Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship. Value of correlation coefficient: Direction of the relationship (positive, negative, or zero relationship): Strength of the relationship (strong/moderate/weak): Question 2: Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size. (The answer for the…arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forwardProblem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?arrow_forward
- We consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forwardQuestion 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forward
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