Using & Understanding Mathematics, Books a la Carte edition (7th Edition)
7th Edition
ISBN: 9780134716015
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Chapter 5.A, Problem 36E
Type of Study. Determine whether the following studies are observational studies or experiments. If the study is an experiment, identify the control and treatment groups, and discuss whether single-or double-blinding is necessary. If the study is observational, state whether it is a case-control study, and if so, identify the cases and controls.
36. A National Cancer Institute study of 716 melanoma patients and 1014 cancer-free patients matched by age, sex, and race found that those having a single large mole had twice the risk of melanoma. Having 10 or more moles was associated with a 12 times greater risk of melanoma (Journal of the American Medical Association).
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In 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.)
3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i,
and i.
(a) Verify the relations between this roots and the coefficients of the polynomial.
(b) Find the annulus region in which the roots lie.
The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c.
Question content area bottom
Part 1
a. Develop a simple linear regression model between billable hours and overhead costs.
Overhead
Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable
Hours
(Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.)
Part 2
b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm?
Interpret the fixed term,
b 0b0,
if appropriate. Choose the correct answer below.
A.
The value of
b 0b0
is the predicted billable hours for an overhead cost of 0 dollars.
B.
It is not appropriate to interpret
b 0b0,
because its value…
Chapter 5 Solutions
Using & Understanding Mathematics, Books a la Carte edition (7th Edition)
Ch. 5.A - You conduct a poll in which you randomly select...Ch. 5.A - Results of the poll described in question 1 would...Ch. 5.A - When we say that a sample is representative of the...Ch. 5.A - A poll concerning support for mass transit is...Ch. 5.A - Consider an experiment designed to test whether...Ch. 5.A - The experiment described in question 4 is a....Ch. 5.A - The purpose of a placebo is a. to prevent...Ch. 5.A - An experiment is single-blind if a. it lacks a...Ch. 5.A - Poll X predicts that Powell will receive 49% of...Ch. 5.A - A survey reveals that 12% of Americans believe...
Ch. 5.A - 1. Why do we say that the term statistics has two...Ch. 5.A - 2. Define the terms populatíon, sample, population...Ch. 5.A - Describe the five basic steps in a statistical...Ch. 5.A - Why is a so important that a statistical study use...Ch. 5.A - Prob. 5ECh. 5.A - Prob. 6ECh. 5.A - What is a placebo? Describe the placebo effect and...Ch. 5.A - What is meant by the margin of error in a survey...Ch. 5.A - In my experimental study, I used a sample that was...Ch. 5.A - I followed all the guidelines for sample selection...Ch. 5.A - I wanted to test the effects of vitamin C on...Ch. 5.A - I don’t believe the results of the experiment...Ch. 5.A - A pollster plans to improve survey results by...Ch. 5.A - By choosing my sample carefully, I can make a good...Ch. 5.A - Population and Sample. For the following studies,...Ch. 5.A - 15–20: Population and Sample. For the following...Ch. 5.A - 15–20: Population and Sample. For the following...Ch. 5.A - In a test of the effectiveness of garlic for...Ch. 5.A - In an Accountemps survey of 150 senior executives,...Ch. 5.A - Population and Sample. For the following studies,...Ch. 5.A - Prob. 21ECh. 5.A - Prob. 22ECh. 5.A - Prob. 23ECh. 5.A - Steps in a Study. Describe how you would apply the...Ch. 5.A - 21-26: Steps in a Study. Describe how you would...Ch. 5.A - Prob. 26ECh. 5.A - Representative Sample? You want to determine the...Ch. 5.A - Representative Sample? You want to determine the...Ch. 5.A - Identify the Sampling Method. Identify the...Ch. 5.A - Identify the Sampling Method. Identify the...Ch. 5.A - Identify the Sampling Method. Identify the...Ch. 5.A - Identify the Sampling Method. Identify the...Ch. 5.A - Identify the Sampling Method. Identify the...Ch. 5.A - Identify the Sampling Method. Identify the...Ch. 5.A - Type of Study. Determine whether the following...Ch. 5.A - Type of Study. Determine whether the following...Ch. 5.A - Type of Study. Determine whether each of the...Ch. 5.A - Type of Study. Determine whether the following...Ch. 5.A - Prob. 39ECh. 5.A - Prob. 40ECh. 5.A - Prob. 41ECh. 5.A - Prob. 42ECh. 5.A - Prob. 43ECh. 5.A - Prob. 44ECh. 5.A - Prob. 45ECh. 5.A - Prob. 46ECh. 5.A - Margin of Error. The following summaries of...Ch. 5.A - A Gallup poll found that 36% of Americans favor a...Ch. 5.A - Margin of Error. The following summaries of...Ch. 5.A - Margin of Error. The following summaries of...Ch. 5.A - Effectiveness of a New Drug. As part of the U.S....Ch. 5.A - Real Studies. Consider the following statistical...Ch. 5.A - Real Studies. Consider the following statistical...Ch. 5.A - Prob. 54ECh. 5.A - 55. A Fox News poll carried out by phone...Ch. 5.A - Prob. 56ECh. 5.A - Prob. 57ECh. 5.A - Prob. 58ECh. 5.A - Statistics in the News. Select three news stories...Ch. 5.A - 62. Statistics in Your Major. Write two to three...Ch. 5.A - Prob. 61ECh. 5.A - Prob. 62ECh. 5.A - 65. Poor Sampling. Find a new article about a...Ch. 5.A - 66. Good Sampling. Find a recent news article that...Ch. 5.A - 67. Margin of Error. Find a report of a recent...Ch. 5.A - Prob. 66ECh. 5.A - Prob. 67ECh. 5.B - You read about an issue that was the subject of an...Ch. 5.B - A study conducted by the oil company Exxon Mobil...Ch. 5.B - Consider a study designed to learn about the...Ch. 5.B - The show The Voice selects winners based on votes...Ch. 5.B - Consider an experiment in which you measure the...Ch. 5.B - Consider a survey in which 1000 people arc asked...Ch. 5.B - Imagine that a survey of randomly selected people...Ch. 5.B - You want to know whether people prefer Smith or...Ch. 5.B - A self-selected survey is one in which a. the...Ch. 5.B - If a statistical study is carefully conducted tn...Ch. 5.B - Prob. 1ECh. 5.B - Prob. 2ECh. 5.B - Prob. 3ECh. 5.B - Prob. 4ECh. 5.B - More than 1 million people sent texts in response...Ch. 5.B - Thc survey of religious beliefs suffered from...Ch. 5.B - My experiment proved beyond a doubt that vitamin C...Ch. 5.B - Everyone who jogs for exercise should try the new...Ch. 5.B - Prob. 9ECh. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - 9-20: Should You Believe This Study? Based solely...Ch. 5.B - 9–20: Should You Believe This Study? Based solely...Ch. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Prob. 14ECh. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Prob. 17ECh. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Prob. 20ECh. 5.B - 21–26: Should You Believe This Claim? Based solely...Ch. 5.B - Prob. 22ECh. 5.B - Prob. 23ECh. 5.B - Prob. 24ECh. 5.B - Prob. 25ECh. 5.B - Should You Believe This Claim? Based solely on the...Ch. 5.B - Prob. 27ECh. 5.B - Prob. 28ECh. 5.B - Bias. Identify at least one potential source of...Ch. 5.B - Prob. 30ECh. 5.B - Bias. Identify at least one potential source of...Ch. 5.B - Prob. 32ECh. 5.B - Prob. 33ECh. 5.B - Prob. 34ECh. 5.B - 35. Its All in the Wording. Princeton Survey...Ch. 5.B - 36. It’s All in the Wording. The Pew Research...Ch. 5.B - Prob. 37ECh. 5.B - Stat-Bytes. Much like sound bytes of news stories,...Ch. 5.B - Prob. 39ECh. 5.B - Prob. 40ECh. 5.B - Prob. 41ECh. 5.B - Prob. 42ECh. 5.B - Accurate Headlines? Consider the following...Ch. 5.B - 43–44: Accurate Headlines? Consider the following...Ch. 5.B - 45. What is the Question? Discuss the differences...Ch. 5.B - 46. Exercise and Dementia. A recent study in the...Ch. 5.B - Prob. 47ECh. 5.B - Prob. 48ECh. 5.B - Prob. 49ECh. 5.B - Prob. 50ECh. 5.B - Prob. 51ECh. 5.C - In a class of 200 students, 50 students received a...Ch. 5.C - For the class described in question 1, what was...Ch. 5.C - Which of the following is an example of...Ch. 5.C - The sizes of the wedges in a pie chart tell you a....Ch. 5.C - You have a table listing ten tourist attractions...Ch. 5.C - In the table of tourist attractions and visitors...Ch. 5.C - You have a list of the GPAs of 100 college...Ch. 5.C - You have a list of the average gasoline price for...Ch. 5.C - A histogram is a. a graph that shows how some...Ch. 5.C - You have a histogram and you want to convert it...Ch. 5.C - Prob. 1ECh. 5.C - Prob. 2ECh. 5.C - Prob. 3ECh. 5.C - Prob. 4ECh. 5.C - Prob. 5ECh. 5.C - 6. What two types of graphs are most common when...Ch. 5.C - I made a frequency table with two columns, one...Ch. 5.C - The relative frequency of B grades in our class...Ch. 5.C - The cumulative frequency of C grades in our class...Ch. 5.C - Your bar graph must be wrong, because you have 10...Ch. 5.C - Your pie chart must be wrong, because when I added...Ch. 5.C - I rearranged the bars on my histogram the tallest...Ch. 5.C - 13-14: Frequency Tables. Make frequency tables for...Ch. 5.C - Prob. 14ECh. 5.C - 15-22: Qualitative versus Quantitative. Determine...Ch. 5.C - Qualitative versus Quantitative. Determine whether...Ch. 5.C - 15-22: Qualitative versus Quantitative. Determine...Ch. 5.C - Qualitative versus Quantitative. Determine whether...Ch. 5.C - Qualitative versus Quantitative. Determine whether...Ch. 5.C - Qualitative versus Quantitative. Determine whether...Ch. 5.C - 15-22: Qualitative versus Quantitative. Determine...Ch. 5.C - Qualitative versus Quantitative. Determine whether...Ch. 5.C - Binned Frequency Tables. Use the given bin sizes...Ch. 5.C - Binned Frequency Tables. Use the given bin sizes...Ch. 5.C - 25. Most Populous Countries. The following table...Ch. 5.C - Prob. 26ECh. 5.C - Prob. 27ECh. 5.C - Prob. 28ECh. 5.C - Prob. 29ECh. 5.C - Prob. 30ECh. 5.C - 31. Cell Phone Subscriptions. The following table...Ch. 5.C - 32. Death Rates. Figure 5.10 is a time-series...Ch. 5.C - U.S. Electrical Energy. The following table gives...Ch. 5.C - Prob. 34ECh. 5.C - Ages of Nobel Prize Winners. The Following...Ch. 5.C - Prob. 36ECh. 5.C - Prob. 37ECh. 5.C - Prob. 38ECh. 5.C - Immigrant Data. The following table gives the...Ch. 5.C - Prob. 40ECh. 5.C - Prob. 41ECh. 5.C - 49. Bar Graph. Find a recent news article tha...Ch. 5.C - 50. Pie Chart. Find a recent news article that...Ch. 5.C - 51. Histogram. Find a recent news article that...Ch. 5.C - 52. Line Chart. Find a recent news article that...Ch. 5.C - Answer the following questions using procedures...Ch. 5.C - 47. U.S. Population in Poverty. Use Excel or with...Ch. 5.C - 48. StatCrunch Data Entry. To gain practice...Ch. 5.C - 49. NFL Data. Open the shared data set called NFL...Ch. 5.C - Prob. 50ECh. 5.D - Based on Figure 5.12, which statement is correct?...Ch. 5.D - Prob. 2QQCh. 5.D - Prob. 3QQCh. 5.D - Prob. 4QQCh. 5.D - Prob. 5QQCh. 5.D - Prob. 6QQCh. 5.D - Which of the following best describes the...Ch. 5.D - Prob. 8QQCh. 5.D - 9. Consider Figure 5.22(a). Moving one tick mark...Ch. 5.D - 10. Consider Figure 5.23(a). In years where the...Ch. 5.D - Briefly describe the construction and use of...Ch. 5.D - What are geographical data? Briefly describe at...Ch. 5.D - What are three-dimensional graphics? Explain the...Ch. 5.D - What are infographics, and what is their goal?Ch. 5.D - Prob. 5ECh. 5.D - 6. What is an exponential scale? When is an...Ch. 5.D - Explain how a graph that shows percentage change...Ch. 5.D - Prob. 8ECh. 5.D - My bar chart contains more information than yours,...Ch. 5.D - 10. I used an exponential scale because the data...Ch. 5.D - Prob. 11ECh. 5.D - A graph showing the yearly rate of increase in the...Ch. 5.D - Educational Value. Use the graphs in Figure 5.11...Ch. 5.D - 13-16: Educational Value. Use the graphs in Figure...Ch. 5.D - Prob. 15ECh. 5.D - Prob. 16ECh. 5.D - Gender and Mathematics. Consider the data...Ch. 5.D - Gender and Science. The following table gives data...Ch. 5.D - Prob. 19ECh. 5.D - Prob. 20ECh. 5.D - Disease Stack Plot. Use Figure 5.14 to answer the...Ch. 5.D - Disease Stack Plot. Use Figure 5.14 to answer the...Ch. 5.D - 23. Figure 5.24 shows a stack plot of federal...Ch. 5.D - 24. College Degrees. Figure 5.25 shows the numbers...Ch. 5.D - 25-26: Melanoma Mortality. Figure 5.26 shows the...Ch. 5.D - Prob. 26ECh. 5.D - Prob. 27ECh. 5.D - Prob. 28ECh. 5.D - Prob. 29ECh. 5.D - Prob. 30ECh. 5.D - Prob. 31ECh. 5.D - Infographic. Use Figure 5.18 to answer the...Ch. 5.D - Volume Distortion. Figure 5.29 depicts the amounts...Ch. 5.D - Three-DimensionaI Pies. The pie charts in Figure...Ch. 5.D - Refugees to Europe. Figure 5.31 shows the numbers...Ch. 5.D - 36. Life Expectancy. Figure 5.32 shows the life...Ch. 5.D - 37. Moore’s Law. Moore law refers to a prediction...Ch. 5.D - Prob. 38ECh. 5.D - Prob. 39ECh. 5.D - Percentage Change in the CPI. Figure 5.33 shows...Ch. 5.D - Prob. 41ECh. 5.D - Prob. 42ECh. 5.D - Prob. 43ECh. 5.D - Prob. 44ECh. 5.D - Prob. 45ECh. 5.D - Prob. 46ECh. 5.D - 47-52: Creating Graphics. Make a graphical display...Ch. 5.D - 47-52: Creating Graphics. Make a graphical display...Ch. 5.D - Creating Graphics. Make a graphical display of the...Ch. 5.D - Prob. 50ECh. 5.D - Prob. 51ECh. 5.D - Prob. 52ECh. 5.D - Prob. 53ECh. 5.D - Prob. 54ECh. 5.D - Prob. 55ECh. 5.D - Prob. 56ECh. 5.D - Prob. 57ECh. 5.D - Prob. 58ECh. 5.D - Prob. 59ECh. 5.D - 46. Interactive Infographics. Find a few examples...Ch. 5.D - Answer the following questions using procedures...Ch. 5.D - Answer the following questions using procedures...Ch. 5.D - Prob. 63ECh. 5.D - Prob. 64ECh. 5.D - Prob. 65ECh. 5.D - Answer the following questions using procedures...Ch. 5.D - Prob. 67ECh. 5.D - Prob. 68ECh. 5.E - If X is correlated with Y, a. X causes Y. b....Ch. 5.E - Figure 5.40. According to this diagram, life...Ch. 5.E - If the points on a scatterplot fall on a nearly...Ch. 5.E - If the points on a scatterplot fall into a broad...Ch. 5.E - When can you rule out the possibility that changes...Ch. 5.E - What type of correlation would you expect between...Ch. 5.E - You have found a higher rate of birth defects...Ch. 5.E - Based on the data in Figure 5.38, abou how much...Ch. 5.E - Which of the following statements best describes...Ch. 5.E - A finding by a jury that a pcrson is guilty...Ch. 5.E - What is a correlation? Give three examples of...Ch. 5.E - What is a scatterplot, and how is one made? How...Ch. 5.E - Prob. 3ECh. 5.E - Describe the three general categories of...Ch. 5.E - 5. Briefly describe each of the six guidelines...Ch. 5.E - Briefly describe three levels of confidence in...Ch. 5.E - There is a strong negative correlation between the...Ch. 5.E - There is a strong positive correlation between the...Ch. 5.E - I found a nearly perfect positive correlation...Ch. 5.E - I found a nearly perfect negative correlation...Ch. 5.E - I had originally suspected that an increase in...Ch. 5.E - Prob. 12ECh. 5.E - Interpreting Scatterplots. Consider the following...Ch. 5.E - Interpreting Scatterplots. Consider the following...Ch. 5.E - Interpreting Scatterplots. Consider the following...Ch. 5.E - Interpreting Scatterplots. Consider the following...Ch. 5.E - Types of Correlation. For the following pairs of...Ch. 5.E - Types of Correlation. For the following pairs of...Ch. 5.E - Types of Correlation. For the following pairs of...Ch. 5.E - Prob. 20ECh. 5.E - Prob. 21ECh. 5.E - Prob. 22ECh. 5.E - 17–24: Types of Correlation. For the following...Ch. 5.E - Prob. 24ECh. 5.E - Prob. 25ECh. 5.E - Making Scatterplots. Consider the following data...Ch. 5.E - Making Scatterplots. Consider the following data...Ch. 5.E - Prob. 28ECh. 5.E - Prob. 29ECh. 5.E - Making Scatterplots. Consider the following data...Ch. 5.E - Federal Aid and Graduation Rates. Figure 5.43...Ch. 5.E - Correlation and Causality. Consider the following...Ch. 5.E - Correlation and Causality. Consider the following...Ch. 5.E - Correlation and Causality. Consider the following...Ch. 5.E - Correlation and Causality. Consider the following...Ch. 5.E - Correlation and Causality. Consider the following...Ch. 5.E - Correlation and Causality. Consider the following...Ch. 5.E - 38. Identifying Causes: Headaches. You are trying...Ch. 5.E - 39. Smoking and Lung Cancer. There is a strong...Ch. 5.E - Prob. 40ECh. 5.E - Prob. 41ECh. 5.E - Prob. 42ECh. 5.E - Prob. 43ECh. 5.E - Prob. 44ECh. 5.E - Prob. 45ECh. 5.E - Prob. 46ECh. 5.E - Prob. 47ECh. 5.E - Answer the following questions using procedures...Ch. 5.E - Exercise and TV Open the shared data set called...Ch. 5.E - 50. StatCrunch Project. Choose one data set...
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