Statistical Reasoning for Everyday Life (5th Edition)
5th Edition
ISBN: 9780134679259
Author: Bennett
Publisher: PEARSON
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Textbook Question
Chapter 2.2, Problem 6E
Does It Make Sense? For Exercises 5–8, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive answers, so your explanation may be more important than your chosen answer.
- 6. Relative Error. Consider the measurements described in Exercise 5. The relative error that the microbiologist makes in measuring a cell must be less than the relative error that the astronomer makes in measuring a galaxy.
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Students have asked these similar questions
4. Suppose that P(X = 1) = P(X = -1) = 1/2, that Y = U(-1, 1) and that X
and Y are independent.
(a) Show, by direct computation, that X + Y = U(-2, 2).
(b) Translate the result to a statement about characteristic functions.
(c) Which well-known trigonometric formula did you discover?
9. The concentration function of a random variable X is defined as
Qx(h) = sup P(x ≤ X ≤x+h), h>0.
x
(a) Show that Qx+b (h) = Qx(h).
(b) Is it true that Qx(ah) =aQx(h)?
(c) Show that, if X and Y are independent random variables, then
Qx+y (h) min{Qx(h). Qy (h)).
To put the concept in perspective, if X1, X2, X, are independent, identically
distributed random variables, and S₁ = Z=1Xk, then there exists an absolute
constant, A, such that
A
Qs, (h) ≤
√n
Some references: [79, 80, 162, 222], and [204], Sect. 1.5.
29
Suppose that a mound-shaped data set has a
must mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 6 and 12?
b. About what percentage of the data should
lie between 4 and 6?
c. About what percentage of the data should
lie below 4?
91002 175/1
3
Chapter 2 Solutions
Statistical Reasoning for Everyday Life (5th Edition)
Ch. 2.1 - Qualitative versus Quantitative. What is the...Ch. 2.1 - Discrete versus Continuous. Distinguish between...Ch. 2.1 - Measurement Levels. What do we mean by data at the...Ch. 2.1 - Interval versus Ratio. Explain why temperatures on...Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...
Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...Ch. 2.1 - Does It Make Sense? For Exercises 58, determine...Ch. 2.1 - Qualitative versus Quantitative Data. In Exercises...Ch. 2.1 - Qualitative versus Quantitative Data. In Exercises...Ch. 2.1 - Discrete or Continuous. In Exercises 1928, state...Ch. 2.1 - Discrete or Continuous. In Exercises 1928, state...Ch. 2.1 - Discrete or Continuous. In Exercises 1928, state...Ch. 2.1 - Discrete or Continuous. In Exercises 1928, state...Ch. 2.1 - Discrete or Continuous. In Exercises 1928, state...Ch. 2.1 - Discrete or Continuous. In Exercises 1928, state...Ch. 2.1 - Discrete or Continuous. In Exercises 1928, state...Ch. 2.1 - Discrete or Continuous. In Exercises 1928, state...Ch. 2.1 - Discrete or Continuous. In Exercises 1928, state...Ch. 2.1 - Discrete or Continuous. In Exercises 1928, state...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Levels of Measurement. For the data described in...Ch. 2.1 - Meaningful Ratios? In Exercises 4148, determine...Ch. 2.1 - Meaningful Ratios? In Exercises 4148, determine...Ch. 2.1 - Meaningful Ratios? In Exercises 4148, determine...Ch. 2.1 - Meaningful Ratios? In Exercises 4148, determine...Ch. 2.1 - Meaningful Ratios? In Exercises 4148, determine...Ch. 2.1 - Meaningful Ratios? In Exercises 4148, determine...Ch. 2.1 - Meaningful Ratios? In Exercises 4148, determine...Ch. 2.1 - Meaningful Ratios? In Exercises 4148, determine...Ch. 2.1 - Complete Classification. In Exercises 4956,...Ch. 2.1 - Complete Classification. In Exercises 4956,...Ch. 2.1 - Complete Classification. In Exercises 4956,...Ch. 2.1 - Complete Classification. In Exercises 4956,...Ch. 2.1 - Prob. 53ECh. 2.1 - Complete Classification. In Exercises 4956,...Ch. 2.1 - Prob. 55ECh. 2.1 - Complete Classification. In Exercises 4956,...Ch. 2.2 - Error Type. Distinguish between random errors and...Ch. 2.2 - Absolute and Relative. Distinguish between the...Ch. 2.2 - Accuracy and Precision. Distinguish between...Ch. 2.2 - Honest Numbers. Why can it be misleading to give...Ch. 2.2 - Does It Make Sense? For Exercises 58, determine...Ch. 2.2 - Does It Make Sense? For Exercises 58, determine...Ch. 2.2 - Does It Make Sense? For Exercises 58, determine...Ch. 2.2 - Does It Make Sense? For Exercises 58, determine...Ch. 2.2 - IRS. An IRS agent reviews tax returns to identify...Ch. 2.2 - Safe Air Travel. Before taking off, a pilot is...Ch. 2.2 - Technical Specifications. A smartphone battery is...Ch. 2.2 - Crime Statistics. Former New York City Police...Ch. 2.2 - Sources of Errors. For each measurement described...Ch. 2.2 - Sources of Errors. For each measurement described...Ch. 2.2 - Sources of Errors. For each measurement described...Ch. 2.2 - Sources of Errors. For each measurement described...Ch. 2.2 - Sources of Errors. For each measurement described...Ch. 2.2 - Sources of Errors. For each measurement described...Ch. 2.2 - Sources of Errors. For each measurement described...Ch. 2.2 - Sources of Errors. For each measurement described...Ch. 2.2 - Absolute and Relative Errors. In Exercises 2124,...Ch. 2.2 - Absolute and Relative Errors. In Exercises 2124,...Ch. 2.2 - Absolute and Relative Errors. In Exercises 2124,...Ch. 2.2 - Absolute and Relative Errors. In Exercises 2124,...Ch. 2.2 - Minimizing Errors. Twenty-five people, including...Ch. 2.2 - Minimizing Errors. When a model 22F car battery is...Ch. 2.2 - Accuracy and Precision in Corvette Weight. A new...Ch. 2.2 - Accuracy and Precision in Height. Assume that your...Ch. 2.2 - Accuracy and Precision in Weight. Suppose your...Ch. 2.2 - Prob. 30ECh. 2.2 - Believable Facts? Exercises 3138 give statements...Ch. 2.2 - Believable Facts? Exercises 3138 give statements...Ch. 2.2 - Prob. 33ECh. 2.2 - Believable Facts? Exercises 3138 give statements...Ch. 2.2 - Prob. 35ECh. 2.2 - Believable Facts? Exercises 3138 give statements...Ch. 2.2 - Believable Facts? Exercises 3138 give statements...Ch. 2.2 - Believable Facts? Exercises 3138 give statements...Ch. 2.3 - Statistical Literacy and Critical Thinking...Ch. 2.3 - Percentage Difference. Distinguish between...Ch. 2.3 - Of versus More Than. Explain the difference...Ch. 2.3 - Percentage Points. Explain the difference between...Ch. 2.3 - Does It Make Sense? For Exercises 58, determine...Ch. 2.3 - Does It Make Sense? For Exercises 58, determine...Ch. 2.3 - Does It Make Sense? For Exercises 58, determine...Ch. 2.3 - Does It Make Sense? For Exercises 58, determine...Ch. 2.3 - Concepts and Applications Fractions, Decimals,...Ch. 2.3 - Fractions, Decimals, Percentages. Express the...Ch. 2.3 - Percentage Practice. A study was conducted of...Ch. 2.3 - Percentage Practice. A study was conducted to...Ch. 2.3 - Percentage of Media commonly report survey...Ch. 2.3 - Percentage. A New York Times editorial criticized...Ch. 2.3 - Relative Change. Exercises 1522 each provide two...Ch. 2.3 - Relative Change. Exercises 1522 each provide two...Ch. 2.3 - Relative Change. Exercises 1522 each provide two...Ch. 2.3 - Relative Change. Exercises 1522 each provide two...Ch. 2.3 - Relative Change. Exercises 1522 each provide two...Ch. 2.3 - Relative Change. Exercises 1522 each provide two...Ch. 2.3 - Relative Change. Exercises 1522 each provide two...Ch. 2.3 - Relative Change. Exercises 1522 each provide two...Ch. 2.3 - Surveys. Some important analyses of survey results...Ch. 2.3 - Surveys. Some important analyses of survey results...Ch. 2.3 - Surveys. Some important analyses of survey results...Ch. 2.3 - Surveys. Some important analyses of survey results...Ch. 2.3 - Of versus More Than. Fill in the blanks in...Ch. 2.3 - Of versus More Than. Fill in the blanks in...Ch. 2.3 - Of versus More Than. Fill in the blanks in...Ch. 2.3 - Of versus More Than. Fill in the blanks in...Ch. 2.3 - Margin of Error. A Gallup poll of 1012 American...Ch. 2.3 - Margin of Error. A Pew Research Center survey of...Ch. 2.3 - Percentages of Percentages. Exercises 3336...Ch. 2.3 - Percentages of Percentages. Exercises 3336...Ch. 2.3 - Percentages of Percentages. Exercises 3336...Ch. 2.3 - Percentages of Percentages. Exercises 3336...Ch. 2.3 - TV Share. A recent Super Bowl football game had a...Ch. 2.3 - Misleading Percentage. In a Gallup poll of 1236...Ch. 2.4 - Index Number. What is an index number? Briefly...Ch. 2.4 - CPI. What is the Consumer Price Index (CPI)? How...Ch. 2.4 - Inflation. In making price comparisons, why is it...Ch. 2.4 - CPI Change. If the CPI increases, must wages also...Ch. 2.4 - Does It Make Sense? For Exercises 58, determine...Ch. 2.4 - Does It Make Sense? For Exercises 58, determine...Ch. 2.4 - Does It Make Sense? For Exercises 58, determine...Ch. 2.4 - Does It Make Sense? For Exercises 58, determine...Ch. 2.4 - Consumer Price Index. In Exercises 916, use the...Ch. 2.4 - Consumer Price Index. In Exercises 916, use the...Ch. 2.4 - Consumer Price Index. In Exercises 916, use the...Ch. 2.4 - Consumer Price Index. In Exercises 916, use the...Ch. 2.4 - Prob. 13ECh. 2.4 - Consumer Price Index. In Exercises 916, use the...Ch. 2.4 - Consumer Price Index. In Exercises 916, use the...Ch. 2.4 - Consumer Price Index. In Exercises 916, use the...Ch. 2.4 - Coffee Index. In Exercises 1720, use the following...Ch. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Coffee Index. In Exercises 1720, use the following...Ch. 2.4 - Pizza Cost and Subway Fare. The pizza connection...Ch. 2.4 - Pizza Cost and Subway Fare. The pizza connection...Ch. 2.4 - Pizza Cost and Subway Fare. The pizza connection...Ch. 2.4 - Pizza Cost and Subway Fare. The pizza connection...Ch. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Housing Price Index. Realtors use an index to...Ch. 2.4 - Prob. 29ECh. 2.4 - Housing Price Index. Realtors use an index to...Ch. 2.4 - Prob. 31ECh. 2.4 - Housing Price Index. Realtors use an index to...Ch. 2 - Germs. In a Wakefield Research survey, 1003...Ch. 2 - Health Care Spending. Total spending on health...Ch. 2 - Prob. 3CRECh. 2 - Minimum Wage. The following table lists the...Ch. 2 - Braking reaction times of 36 randomly selected...Ch. 2 - What is the level of measurement of the values...Ch. 2 - Prob. 3CQCh. 2 - A researcher measures the braking reaction time of...Ch. 2 - Braking reaction times of 36 randomly selected...Ch. 2 - Recorded survey results include the states in...Ch. 2 - Prob. 7CQCh. 2 - Prob. 8CQCh. 2 - Prob. 9CQCh. 2 - Prob. 10CQCh. 2 - Politics Who Benefited Most from Lower Tax Rates?...Ch. 2 - Prob. 1.2FCh. 2 - Prob. 1.3F
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- 2,3, ample and rical t? the 28 Suppose that a mound-shaped data set has a mean of 10 and standard deviation of 2. a. About what percentage of the data should lie between 8 and 12? b. About what percentage of the data should lie above 10? c. About what percentage of the data should lie above 12?arrow_forward27 Suppose that you have a data set of 1, 2, 2, 3, 3, 3, 4, 4, 5, and you assume that this sample represents a population. The mean is 3 and g the standard deviation is 1.225.10 a. Explain why you can apply the empirical rule to this data set. b. Where would "most of the values" in the population fall, based on this data set?arrow_forward30 Explain how you can use the empirical rule to find out whether a data set is mound- shaped, using only the values of the data themselves (no histogram available).arrow_forward
- 5. Let X be a positive random variable with finite variance, and let A = (0, 1). Prove that P(X AEX) 2 (1-A)² (EX)² EX2arrow_forward6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows: P(X=-x) = P(X = x)=p. P(X=0)= 1-2p. Show that there is equality in Chebyshev's inequality for X. This means that Chebyshev's inequality, in spite of being rather crude, cannot be improved without additional assumptions.arrow_forward4. Prove that, for any random variable X, the minimum of EIX-al is attained for a = med (X).arrow_forward
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