7th Edition

ISBN: 9780135239919

Author: BENNETT AND BR

Publisher: PEARSON

Concept explainers

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Textbook Question

Chapter 5.E, Problem 4E

Describe the three general categories of explanation for a correlation. Give an example of each.

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Chapter 5.E, Problem 3E

Chapter 5.E, Problem 5E

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Total marks 15 3. (i) Let FRN Rm be a mapping and x = RN is a given point. Which of the following statements are true? Construct counterex- amples for any that are false. (a) If F is continuous at x then F is differentiable at x. (b) If F is differentiable at x then F is continuous at x. If F is differentiable at x then F has all 1st order partial (c) derivatives at x. (d) If all 1st order partial derivatives of F exist and are con- tinuous on RN then F is differentiable at x. [5 Marks] (ii) Let mappings F= (F1, F2) R³ → R² and G=(G1, G2) R² → R² : be defined by F₁ (x1, x2, x3) = x1 + x², G1(1, 2) = 31, F2(x1, x2, x3) = x² + x3, G2(1, 2)=sin(1+ y2). By using the chain rule, calculate the Jacobian matrix of the mapping GoF R3 R², i.e., JGoF(x1, x2, x3). What is JGOF(0, 0, 0)? (iii) [7 Marks] Give reasons why the mapping Go F is differentiable at (0, 0, 0) R³ and determine the derivative matrix D(GF)(0, 0, 0). [3 Marks]

5. (i) Let f R2 R be defined by f(x1, x2) = x² - 4x1x2 + 2x3. Find all local minima of f on R². (ii) [10 Marks] Give an example of a function f: R2 R which is not bounded above and has exactly one critical point, which is a minimum. Justify briefly Total marks 15 your answer. [5 Marks]

Total marks 15 4. : Let f R2 R be defined by f(x1, x2) = 2x²- 8x1x2+4x+2. Find all local minima of f on R². [10 Marks] (ii) Give an example of a function f R2 R which is neither bounded below nor bounded above, and has no critical point. Justify briefly your answer. [5 Marks]

Chapter 5 Solutions

USING AND UNDERSTANDING MATHEMATICS W/

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. 5E Ch. 5.A - Prob. 6E Ch. 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. 21E Ch. 5.A - Prob. 22E Ch. 5.A - Prob. 23E Ch. 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. 26E Ch. 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. 39E Ch. 5.A - Prob. 40E Ch. 5.A - Prob. 41E Ch. 5.A - Prob. 42E Ch. 5.A - Prob. 43E Ch. 5.A - Prob. 44E Ch. 5.A - Prob. 45E Ch. 5.A - Prob. 46E Ch. 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. 54E Ch. 5.A - 55. A Fox News poll carried out by phone...Ch. 5.A - Prob. 56E Ch. 5.A - Prob. 57E Ch. 5.A - Prob. 58E Ch. 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. 61E Ch. 5.A - Prob. 62E Ch. 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. 66E Ch. 5.A - Prob. 67E Ch. 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. 1E Ch. 5.B - Prob. 2E Ch. 5.B - Prob. 3E Ch. 5.B - Prob. 4E Ch. 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. 9E Ch. 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. 14E Ch. 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. 17E Ch. 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. 20E Ch. 5.B - 21–26: Should You Believe This Claim? Based solely...Ch. 5.B - Prob. 22E Ch. 5.B - Prob. 23E Ch. 5.B - Prob. 24E Ch. 5.B - Prob. 25E Ch. 5.B - Should You Believe This Claim? Based solely on the...Ch. 5.B - Prob. 27E Ch. 5.B - Prob. 28E Ch. 5.B - Bias. Identify at least one potential source of...Ch. 5.B - Prob. 30E Ch. 5.B - Bias. Identify at least one potential source of...Ch. 5.B - Prob. 32E Ch. 5.B - Prob. 33E Ch. 5.B - Prob. 34E Ch. 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. 37E Ch. 5.B - Stat-Bytes. Much like sound bytes of news stories,...Ch. 5.B - Prob. 39E Ch. 5.B - Prob. 40E Ch. 5.B - Prob. 41E Ch. 5.B - Prob. 42E Ch. 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. 47E Ch. 5.B - Prob. 48E Ch. 5.B - Prob. 49E Ch. 5.B - Prob. 50E Ch. 5.B - Prob. 51E Ch. 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. 1E Ch. 5.C - Prob. 2E Ch. 5.C - Prob. 3E Ch. 5.C - Prob. 4E Ch. 5.C - Prob. 5E Ch. 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. 14E Ch. 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. 26E Ch. 5.C - Prob. 27E Ch. 5.C - Prob. 28E Ch. 5.C - Prob. 29E Ch. 5.C - Prob. 30E Ch. 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. 34E Ch. 5.C - Ages of Nobel Prize Winners. The Following...Ch. 5.C - Prob. 36E Ch. 5.C - Prob. 37E Ch. 5.C - Prob. 38E Ch. 5.C - Immigrant Data. The following table gives the...Ch. 5.C - Prob. 40E Ch. 5.C - Prob. 41E Ch. 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. 50E Ch. 5.D - Based on Figure 5.12, which statement is correct?...Ch. 5.D - Prob. 2QQ Ch. 5.D - Prob. 3QQ Ch. 5.D - Prob. 4QQ Ch. 5.D - Prob. 5QQ Ch. 5.D - Prob. 6QQ Ch. 5.D - Which of the following best describes the...Ch. 5.D - Prob. 8QQ Ch. 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. 5E Ch. 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. 8E Ch. 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. 11E Ch. 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. 15E Ch. 5.D - Prob. 16E Ch. 5.D - Gender and Mathematics. Consider the data...Ch. 5.D - Gender and Science. The following table gives data...Ch. 5.D - Prob. 19E Ch. 5.D - Prob. 20E Ch. 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. 26E Ch. 5.D - Prob. 27E Ch. 5.D - Prob. 28E Ch. 5.D - Prob. 29E Ch. 5.D - Prob. 30E Ch. 5.D - Prob. 31E Ch. 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. 38E Ch. 5.D - Prob. 39E Ch. 5.D - Percentage Change in the CPI. Figure 5.33 shows...Ch. 5.D - Prob. 41E Ch. 5.D - Prob. 42E Ch. 5.D - Prob. 43E Ch. 5.D - Prob. 44E Ch. 5.D - Prob. 45E Ch. 5.D - Prob. 46E Ch. 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. 50E Ch. 5.D - Prob. 51E Ch. 5.D - Prob. 52E Ch. 5.D - Prob. 53E Ch. 5.D - Prob. 54E Ch. 5.D - Prob. 55E Ch. 5.D - Prob. 56E Ch. 5.D - Prob. 57E Ch. 5.D - Prob. 58E Ch. 5.D - Prob. 59E Ch. 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. 63E Ch. 5.D - Prob. 64E Ch. 5.D - Prob. 65E Ch. 5.D - Answer the following questions using procedures...Ch. 5.D - Prob. 67E Ch. 5.D - Prob. 68E Ch. 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. 3E Ch. 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. 12E 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 - 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. 20E Ch. 5.E - Prob. 21E Ch. 5.E - Prob. 22E Ch. 5.E - 17–24: Types of Correlation. For the following...Ch. 5.E - Prob. 24E Ch. 5.E - Prob. 25E Ch. 5.E - Making Scatterplots. Consider the following data...Ch. 5.E - Making Scatterplots. Consider the following data...Ch. 5.E - Prob. 28E Ch. 5.E - Prob. 29E Ch. 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. 40E Ch. 5.E - Prob. 41E Ch. 5.E - Prob. 42E Ch. 5.E - Prob. 43E Ch. 5.E - Prob. 44E Ch. 5.E - Prob. 45E Ch. 5.E - Prob. 46E Ch. 5.E - Prob. 47E Ch. 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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Describe the three general categories of explanation for a correlation . Give an example of each.

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Chapter 5 Solutions