7th Edition

ISBN: 9780135239919

Author: BENNETT AND BR

Publisher: PEARSON

Concept explainers

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A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow compar…

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Textbook Question

Chapter 6.B, Problem 18E

Comparing Variations. Consider the following data sets.

a. Find the mean, median and range for each of the two data sets.

b. Give the five-number summary and draw a boxplot for each of the two data sets.

c. Find the standard deviation for each of the two data sets.

d. Apply the range rule of thumb to estimate the standard deviation of each of the two data sets. How well does the rule work in each case? Briefly discuss why it does or does not work well.

e. Based on all your results compare and discuss the two data sets in terms of their center and variation.

18. The following data sets give the approximate lengths of Beethoven’s nine symphonies and nine symphonies (in minutes).

Beethoven:	28	36	50	33	30	40	38	26	68
Mahler:	52	85	94	50	72	72	80	90	80

Chapter 6.B, Problem 18E, Comparing Variations. Consider the following data sets. a. Find the mean, median and range for each

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Chapter 6.B, Problem 17E

Chapter 6.B, Problem 19E

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Use the Euclidean algorithm to find two sets of integers (a, b, c) such that 55a65b+143c: Solution = 1. By the Euclidean algorithm, we have: 143 = 2.65 + 13 and 65 = 5.13, so 13 = 143 – 2.65. - Also, 55 = 4.13+3, 13 = 4.3 + 1 and 3 = 3.1, so 1 = 13 — 4.3 = 13 — 4(55 – 4.13) = 17.13 – 4.55. Combining these, we have: 1 = 17(143 – 2.65) - 4.55 = −4.55 - 34.65 + 17.143, so we can take a = − −4, b = −34, c = 17. By carrying out the division algorithm in other ways, we obtain different solutions, such as 19.55 23.65 +7.143, so a = = 9, b -23, c = 7. = = how ? come [Note that 13.55 + 11.65 - 10.143 0, so we can obtain new solutions by adding multiples of this equation, or similar equations.]

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Chapter 6 Solutions

USING AND UNDERSTANDING MATHEMATICS W/

Ch. 6.A - Prob. 1QQ Ch. 6.A - On an astronomy exam, 20 students score below 79...Ch. 6.A - One hundred students take a chemistry exam. All...Ch. 6.A - Twenty students take a political science exam....Ch. 6.A - A survey asks students to state many sodas they...Ch. 6.A - Among professional actors, a small number of...Ch. 6.A - The distribution of wages at a company is...Ch. 6.A - Compared to a distribution with a broad central...Ch. 6.A - If you compared the distribution of weights of 20...Ch. 6.A - The mayor of a town is considering a run for...

Ch. 6.A - 1. Define and distinguish among mean, median, and...Ch. 6.A - Prob. 2E Ch. 6.A - Briefly describe at least two possible sources of...Ch. 6.A - Prob. 4E Ch. 6.A - Prob. 5E Ch. 6.A - Prob. 6E Ch. 6.A - In my data set of 10 exam scores, the mean turned...Ch. 6.A - In my data set of 10 exam scores, the median...Ch. 6.A - I made a distribution of 15 apartment rents in my...Ch. 6.A - Two extremely tall people skewed the distribution...Ch. 6.A - The distribution of grades was left-skewed, but...Ch. 6.A - There’s much more variation in the ages of the...Ch. 6.A - 13-18: Mean, Median, and Mode. Compute the mean,...Ch. 6.A - Mean, Median, and Mode. Compute the mean, median,...Ch. 6.A - Mean, Median, and Mode. Compute the mean, median,...Ch. 6.A - Mean, Median, and Mode. Compute the mean, median,...Ch. 6.A - 13–18: Mean, Median, and Mode. Compute the mean,...Ch. 6.A - 13-18: Mean, Median, and Mode. Compute the mean,...Ch. 6.A - Outlier Coke. Cans of Coca-Cola vary slightly in...Ch. 6.A - 20. Margin of Victory. The following data give the...Ch. 6.A - Appropriate Average. For each of the following...Ch. 6.A - 21-26: Appropriate Average. For each of the...Ch. 6.A - 21-26: Appropriate Average. For each of the...Ch. 6.A - 21-26: Appropriate Average. For each of the...Ch. 6.A - 21-26: Appropriate Average. For each of the...Ch. 6.A - 21-26: Appropriate Average. For each of the...Ch. 6.A - 27-34: Describing Distributions Consider the...Ch. 6.A - Describing Distributions. Consider the following...Ch. 6.A - 27-34: Describing Distributions Consider the...Ch. 6.A - Describing Distributions. Consider the following...Ch. 6.A - 27-34: Describing Distributions Consider the...Ch. 6.A - Describing Distributions. Consider the following...Ch. 6.A - Prob. 33E Ch. 6.A - Describing Distributions. Consider the following...Ch. 6.A - Prob. 35E Ch. 6.A - 35-36: Understanding Distributions. For the given...Ch. 6.A - Smooth Distributions. Through each histogram, draw...Ch. 6.A - Smooth Distributions. For each histogram, draw a...Ch. 6.A - Smooth Distributions. For each histogram, draw a...Ch. 6.A - Prob. 40E Ch. 6.A - Family Income. Suppose you study family income in...Ch. 6.A - Airline Delays. Suppose you are a scheduler for a...Ch. 6.A - Weighted Means. We often deal with weighted means,...Ch. 6.A - Weighted Means. We often deal with weighted means,...Ch. 6.A - Prob. 45E Ch. 6.A - Prob. 46E Ch. 6.A - Prob. 47E Ch. 6.A - Prob. 48E Ch. 6.A - 50. Daily Averages. Cite three examples of...Ch. 6.A - 51. Distributions in the News. Find three recent...Ch. 6.A - Answer the following questions using procedures...Ch. 6.A - Prob. 52E Ch. 6.A - 53. StatCrunch Project. Choose a data set...Ch. 6.B - The lowest score on an exam was 62, the median...Ch. 6.B - Which of the following is not part of a...Ch. 6.B - The lower quartile for hourly wages at a coffee...Ch. 6.B - Is it possible for a distribution to have a mean...Ch. 6.B - Suppose you are given the mean and just one data...Ch. 6.B - The standard deviation is best described as a...Ch. 6.B - What type of data distribution has a negative...Ch. 6.B - In any distribution, it is always true that a. the...Ch. 6.B - Which data set would you expect to have the...Ch. 6.B - Professors Smith, Jones, and Garcia all got the...Ch. 6.B - Consider two grocery stores at which the mean time...Ch. 6.B - Describe how we define and calculate the range of...Ch. 6.B - Prob. 3E Ch. 6.B - Prob. 4E Ch. 6.B - Prob. 5E Ch. 6.B - Prob. 6E Ch. 6.B - The distributions of scores on two exams had the...Ch. 6.B - The highest exam score was in the upper quartile...Ch. 6.B - For the 30 students who took the test, the high...Ch. 6.B - I examined the data carefully, and the range was...Ch. 6.B - The standard deviation for the heights of a group...Ch. 6.B - The mean gas mileage of the compact cars we tested...Ch. 6.B - 13. Big Bank Verification. Find the mean and...Ch. 6.B - Prob. 14E Ch. 6.B - Comparing Variations. Consider the following data...Ch. 6.B - Prob. 16E Ch. 6.B - Prob. 17E Ch. 6.B - Comparing Variations. Consider the following data...Ch. 6.B - Understanding Variation. The following exercises...Ch. 6.B - Understanding Variation. The following exercises...Ch. 6.B - Pizza Deliveries. After recording the pizza...Ch. 6.B - Airline Arrival Times. Two airlines have data on...Ch. 6.B - 23. Portfolio Standard Deviation. The book...Ch. 6.B - Defect Rates. Two factories each produce 1000...Ch. 6.B - 25. Ice Cream Deviations. Each night you total the...Ch. 6.B - Vet Data. A small animal veterinarian reviews her...Ch. 6.B - Prob. 27E Ch. 6.B - Prob. 28E Ch. 6.B - 29. Quality Control. An auto transmission...Ch. 6.B - Web Data Sets. Go to any website that gives data...Ch. 6.B - Prob. 31E Ch. 6.B - Prob. 32E Ch. 6.B - Prob. 33E Ch. 6.B - Prob. 34E Ch. 6.B - 35. Variation in StatCrunch. Load the data set...Ch. 6.B - 36. StatCrunch Project. Choose a data set...Ch. 6.C - Graphs of normal distributions a. always look...Ch. 6.C - In a normal distribution, the mean a. is equal to...Ch. 6.C - In a normal distribution, data values farther from...Ch. 6.C - Consider wages at a fast food restaurant where...Ch. 6.C - In a normal distribution, about 2/3 Of the data...Ch. 6.C - Suppose a car driven under different conditions...Ch. 6.C - Consider again the car described in Question 6. On...Ch. 6.C - Consider an exam with a normal distribution of...Ch. 6.C - An acquaintance tells you that his IQ is in the...Ch. 6.C - The height of a particular 7-year-old girl has a...Ch. 6.C - 1. What is a normal distribution? Briefly describe...Ch. 6.C - 2. What is the 68-95-99.7 rule for normal...Ch. 6.C - 3. What is a standard score? How do you find the...Ch. 6.C - Prob. 4E Ch. 6.C - The heights of male basketball players at Kentucky...Ch. 6.C - The weights of babies born at Belmont Hospital are...Ch. 6.C - The weights of babies born at Belmont Hospital are...Ch. 6.C - On yesterday's mathematics exam, the standard...Ch. 6.C - My professor graded the final on a curve, and she...Ch. 6.C - Jack is the 50th percentile for height, so he is...Ch. 6.C - Prob. 11E Ch. 6.C - Prob. 12E Ch. 6.C - Prob. 13E Ch. 6.C - 13-18: Normal Distributions. State, with an...Ch. 6.C - 13-18: Normal Distributions. State, with an...Ch. 6.C - Normal Distributions. State, with an explanation,...Ch. 6.C - Prob. 17E Ch. 6.C - 13-18: Normal Distributions. State, with an...Ch. 6.C - The 68-95-99.7 Rule. A set of test scores is...Ch. 6.C - The 68-95-99.7 Rule. The resting heart rates for a...Ch. 6.C - Psychology Exam. The scores on a psychology exam...Ch. 6.C - Psychology Exam. The scores on a psychology exam...Ch. 6.C - Psychology Exam. The scores on a psychology exam...Ch. 6.C - Psychology Exam. The scores on a psychology exam...Ch. 6.C - Psychology Exam. The scores on a psychology exam...Ch. 6.C - 21-28: Psychology Exam. The scores on a psychology...Ch. 6.C - 21-28: Psychology Exam. The scores on a psychology...Ch. 6.C - Psychology Exam. The scores on a psychology exam...Ch. 6.C - Standard Scores and Percentiles. Use Table 6.3 to...Ch. 6.C - Standard Scores and Percentiles. Use Table 6.3 to...Ch. 6.C - Percentiles. Use Table 6.4 to find the approximate...Ch. 6.C - Percentiles. Use Table 6.4 to find the approximate...Ch. 6.C - Pregnancy Length. Actual lengths of terms are...Ch. 6.C - Pregnancy Length. Actual lengths of terms are...Ch. 6.C - Prob. 35E Ch. 6.C - Prob. 36E Ch. 6.C - Heights. According to data from the National...Ch. 6.C - Body Mass Index (BMI). The body mass indexes of...Ch. 6.C - 39. Is It Likely? Suppose you read that the...Ch. 6.C - Prob. 40E Ch. 6.C - GRE Scores. Scores on the verbal Graduate Record...Ch. 6.C - 41-47: GRE Scores. Scores on the verbal section of...Ch. 6.C - 41-47: GRE Scores. Scores on the verbal section of...Ch. 6.C - Prob. 44E Ch. 6.C - 41-47: GRE Scores. Scores on the verbal section of...Ch. 6.C - Prob. 46E Ch. 6.C - Prob. 47E Ch. 6.C - Normal Distributions. Many data sets described in...Ch. 6.C - Normal Demonstration. Do a Web search on the...Ch. 6.C - Heights of American Men. The heights of American...Ch. 6.C - Normal Distributions in StatCrunch. Go to the work...Ch. 6.C - Prob. 52E Ch. 6.D - Prob. 1QQ Ch. 6.D - Prob. 2QQ Ch. 6.D - Prob. 3QQ Ch. 6.D - Prob. 4QQ Ch. 6.D - A poll finds that 35% of the people surveyed...Ch. 6.D - Prob. 6QQ Ch. 6.D - Consider a survey with a margin of error of 4%. If...Ch. 6.D - Prob. 8QQ Ch. 6.D - Prob. 9QQ Ch. 6.D - Prob. 10QQ Ch. 6.D - Prob. 1E Ch. 6.D - Prob. 2E Ch. 6.D - Prob. 3E Ch. 6.D - Prob. 4E Ch. 6.D - Prob. 5E Ch. 6.D - Prob. 6E Ch. 6.D - Prob. 7E Ch. 6.D - Prob. 8E Ch. 6.D - Prob. 9E Ch. 6.D - Prob. 10E Ch. 6.D - Both agencies conducted their surveys carefully,...Ch. 6.D - If you want to reduce the margin of error in your...Ch. 6.D - Prob. 13E Ch. 6.D - Prob. 14E Ch. 6.D - Prob. 15E Ch. 6.D - Subjective Significance. For each of the following...Ch. 6.D - 15-20: Subjective Significance. For each of the...Ch. 6.D - Prob. 18E Ch. 6.D - Prob. 19E Ch. 6.D - 15-20: Subjective Significance. For each of the...Ch. 6.D - Human Body Temperature. A study by University of...Ch. 6.D - Seat Belts and Children. In a study of children...Ch. 6.D - SAT Preparation. A study of 75 students who took...Ch. 6.D - Weight by Age. A National Health Survey determined...Ch. 6.D - Margin of Error. Find the margin of error and the...Ch. 6.D - Prob. 26E Ch. 6.D - 25-32: Margin of Error. Find the margin of error...Ch. 6.D - Prob. 28E Ch. 6.D - Prob. 29E Ch. 6.D - 25-32: Margin of Error. Find the margin of error...Ch. 6.D - 25-32: Margin of Error. Find the margin of error...Ch. 6.D - Margin of Error. Find the margin of error and the...Ch. 6.D - 33-38: Formulating Hypotheses. Consider the...Ch. 6.D - Prob. 34E Ch. 6.D - Prob. 35E Ch. 6.D - Prob. 36E Ch. 6.D - Prob. 37E Ch. 6.D - Prob. 38E Ch. 6.D - 39-44: Hypothesis Tests. The following exercises...Ch. 6.D - 39-44: Hypothesis Tests. The following exercises...Ch. 6.D - 39-44: Hypothesis Tests. The following exercises...Ch. 6.D - 39-44: Hypothesis Tests. The following exercises...Ch. 6.D - 39-44: Hypothesis Tests. The following exercises...Ch. 6.D - Prob. 44E Ch. 6.D - Prob. 45E Ch. 6.D - Prob. 46E Ch. 6.D - Prob. 47E Ch. 6.D - Better Margin of Error. Suppose you want to...Ch. 6.D - Prob. 49E Ch. 6.D - Recent Polls. Visit the websites of polling...Ch. 6.D - Prob. 51E Ch. 6.D - Statistical Significance. Find a recent news...Ch. 6.D - Prob. 53E Ch. 6.D - Hypothesis Testing. Find a news report describing...Ch. 6.D - 55. Confidence Interval. Go to and choose...

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