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 5.3, Problem 32PB
a.
To determine
Define the events.
Identify the conditional probabilities among the four probabilities.
b.
To determine
Compute the
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Here is data with as the response variable.
x y54.4 19.124.9 99.334.5 9.476.6 0.359.4 4.554.4 0.139.2 56.354 15.773.8 9-156.1 319.2Make a scatter plot of this data. Which point is an outlier? Enter as an ordered pair, e.g., (x,y). (x,y)=
Find the regression equation for the data set without the outlier. Enter the equation of the form mx+b rounded to three decimal places. y_wo=
Find the regression equation for the data set with the outlier. Enter the equation of the form mx+b rounded to three decimal places. y_w=
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
Chapter 5 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Ch. 5.1 - Probability Explain what is meant by the long-run...Ch. 5.1 - Testing a coin Your friend decides to flip a coin...Ch. 5.1 - Vegetarianism You randomly sample 10 people in...Ch. 5.1 - Airline accident deaths Airplane safety has been...Ch. 5.1 - World Cup 2014 The powerrank.com website...Ch. 5.1 - Random digits Consider a random number generator...Ch. 5.1 - Polls and sample size A pollster agency wants to...Ch. 5.1 - Heart transplant Before the first human heart...Ch. 5.1 - Nuclear war You are asked to use your best...Ch. 5.1 - Simulate coin flips Use the web app Random Numbers...
Ch. 5.1 - Unannounced pop quiz A teacher announces a pop...Ch. 5.2 - Student union poll Part of a student opinion poll...Ch. 5.2 - Random digit A single random digit (from 09) is...Ch. 5.2 - Pop quiz A teacher gives a four-question...Ch. 5.2 - More true-false questions Your teacher gives a...Ch. 5.2 - Rolling two dice Some friends are playing a game...Ch. 5.2 - Two girls A couple plans to have two children....Ch. 5.2 - Three children A couple plans to have three...Ch. 5.2 - Wrong sample space A couple plans to have four...Ch. 5.2 - Insurance Every year the insurance industry spends...Ch. 5.2 - Cell phone and case At the local cell phone store,...Ch. 5.2 - Seat belt use and auto accidents Based on records...Ch. 5.2 - Protecting the environment When the General Social...Ch. 5.2 - Prob. 25PBCh. 5.2 - Newspaper sales You are the director of newspaper...Ch. 5.2 - Prob. 27PBCh. 5.3 - Recidivism rates A 2014 article from Business...Ch. 5.3 - Prob. 29PBCh. 5.3 - Audit and low income Table 5.3 on audit status and...Ch. 5.3 - Religious affiliation The 2012 Statistical...Ch. 5.3 - Prob. 32PBCh. 5.3 - Prob. 33PBCh. 5.3 - Go Celtics! Larry Bird, who played pro basketball...Ch. 5.3 - Prob. 35PBCh. 5.3 - Homeland security According to an article in The...Ch. 5.3 - Down syndrome again Example 8 discussed the Triple...Ch. 5.3 - Prob. 38PBCh. 5.3 - Happiness in relationship Are people happy in...Ch. 5.3 - Prob. 40PBCh. 5.3 - Prob. 41PBCh. 5.3 - Prob. 42PBCh. 5.3 - Prob. 43PBCh. 5.3 - Prob. 44PBCh. 5.3 - Family with two children For a family with two...Ch. 5.3 - Prob. 46PBCh. 5.4 - Birthdays of presidents Of the first 44 presidents...Ch. 5.4 - Prob. 48PBCh. 5.4 - Lots of pairs Show that with 25 students, there...Ch. 5.4 - Prob. 50PBCh. 5.4 - Prob. 51PBCh. 5.4 - Prob. 52PBCh. 5.4 - Coincidence in your life State an event that has...Ch. 5.4 - Monkeys typing Shakespeare Since events of low...Ch. 5.4 - A true coincidence at DisneyWorld Wisconsin has...Ch. 5.4 - Prob. 56PBCh. 5.4 - Mammogram diagnostics Breast cancer is the most...Ch. 5.4 - Prob. 58PBCh. 5.4 - Prob. 59PBCh. 5.4 - Convicted by mistake In criminal trials (e.g.,...Ch. 5.4 - DNA evidence compelling? DNA evidence can be...Ch. 5.4 - Prob. 62PBCh. 5.4 - Simulating donations to local blood bank The...Ch. 5.4 - Probability of winning In Example 16, we estimated...Ch. 5 - Peyton Manning completions As of the end of the...Ch. 5 - Due for a boy? A couple has five children, all...Ch. 5 - Prob. 68CPCh. 5 - Choices for lunch For the set lunch at Amelias...Ch. 5 - Caught doctoring the books After the major...Ch. 5 - Life after death In a General Social Survey, in...Ch. 5 - Death penalty jury In arguing against the death...Ch. 5 - Drivers exam Three 15-year-old friends with no...Ch. 5 - Prob. 74CPCh. 5 - Health insurance According to a 2006 census bureau...Ch. 5 - Prob. 76CPCh. 5 - Prob. 77CPCh. 5 - Prob. 78CPCh. 5 - Prob. 79CPCh. 5 - Roll two more dice Refer to the previous exercise....Ch. 5 - Prob. 81CPCh. 5 - Waste dump sites A federal agency is deciding...Ch. 5 - Prob. 83CPCh. 5 - Prob. 84CPCh. 5 - Prob. 85CPCh. 5 - Death penalty and false positives For the decision...Ch. 5 - Prob. 87CPCh. 5 - Screening for heart attacks Biochemical markers...Ch. 5 - Prob. 89CPCh. 5 - Color blindness For genetic reasons, color...Ch. 5 - Prob. 91CPCh. 5 - Prostate cancer A study of the PSA blood test for...Ch. 5 - Prob. 95CPCh. 5 - Illustrate probability terms with scenarios a....Ch. 5 - Short term versus long run Short-term aberrations...Ch. 5 - Prob. 98CPCh. 5 - Mrs. Test Mrs. Test (see www.mrstest.com) sells...Ch. 5 - Prob. 100CPCh. 5 - Prob. 101CPCh. 5 - Prob. 102CPCh. 5 - Protective bomb Before the days of high security...Ch. 5 - Streak shooter Sportscaster Maria Coselli claims...Ch. 5 - Multiple choice Choose ALL correct responses. For...Ch. 5 - Prob. 106CPCh. 5 - Prob. 107CPCh. 5 - Multiple choice: Dream come true You have a dream...Ch. 5 - Prob. 109CPCh. 5 - True or false Answer true of false for each part....Ch. 5 - True or false When you flip a balanced coin twice,...Ch. 5 - Prob. 112CPCh. 5 - Prob. 113CPCh. 5 - Prob. 114CPCh. 5 - Prob. 115CPCh. 5 - Prob. 116CP
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- 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.arrow_forwardOne 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_forward
- 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. 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_forwardDoes 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_forward
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