Solutions Manual - for Engineering and the Sciences NINTH EDITION ...

Solutions Manual For Probability and Statistics for Engineering and the Sciences

NINTH EDITION

Jay Devore Prepared by Matthew A. Carlton

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1

CHAPTER 1

Section 1.1

1.

• Los Angeles Times, Oberlin Tribune, Gainesville Sun, Washington Post

• Duke Energy, Clorox, Seagate, Neiman Marcus

• Vince Correa, Catherine Miller, Michael Cutler, Ken Lee

• 2.97, 3.56, 2.20, 2.97

2.

• 29.1 yd, 28.3 yd, 24.7 yd, 31.0 yd

• 432 pp, 196 pp, 184 pp, 321 pp

• 2.1, 4.0, 3.2, 6.3

• 0.07 g, 1.58 g, 7.1 g, 27.2 g

3.

• How likely is it that more than half of the sampled computers will need or have needed

warranty service? What is the expected number among the 100 that need warranty service? How likely is it that the number needing warranty service will exceed the expected number by more than 10?

• Suppose that 15 of the 100 sampled needed warranty service. How confident can we be

that the proportion of all such computers needing warranty service is between .08 and .22? Does the sample provide compelling evidence for concluding that more than 10% of all such computers need warranty service?

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Chapter 1: Overview and Descriptive Statistics

2 4.

• Concrete populations: all living U.S. Citizens, all mutual funds marketed in the U.S., all

books published in 1980 Hypothetical populations: all grade point averages for University of California undergraduates during the next academic year, page lengths for all books published during the next calendar year, batting averages for all major league players during the next baseball season

• (Concrete) Probability: In a sample of 5 mutual funds, what is the chance that all 5 have

rates of return which exceeded 10% last year?Statistics: If previous year rates-of-return for 5 mutual funds were 9.6, 14.5, 8.3, 9.9 and 10.2, can we conclude that the average rate for all funds was below 10%?(Hypothetical) Probability: In a sample of 10 books to be published next year, how likely is it that the average number of pages for the 10 is between 200 and 250?Statistics: If the sample average number of pages for 10 books is 227, can we be highly confident that the average for all books is between 200 and 245?

5.

• No. All students taking a large statistics course who participate in an SI program of this

sort.

• The advantage to randomly allocating students to the two groups is that the two groups

should then be fairly comparable before the study. If the two groups perform differently in the class, we might attribute this to the treatments (SI and control). If it were left to students to choose, stronger or more dedicated students might gravitate toward SI, confounding the results.

• If all students were put in the treatment group, there would be no firm basis for assessing

the effectiveness of SI (nothing to which the SI scores could reasonably be compared).

• One could take a simple random sample of students from all students in the California State

University system and ask each student in the sample to report the distance form their hometown to campus. Alternatively, the sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.Certain problems might arise with self reporting of distances, such as recording error or poor recall. This study is enumerative because there exists a finite, identifiable population of objects from which to sample.

• One could generate a simple random sample of all single-family homes in the city, or a

stratified random sample by taking a simple random sample from each of the 10 district neighborhoods. From each of the selected homes, values of all desired variables would be determined. This would be an enumerative study because there exists a finite, identifiable population of objects from which to sample.

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Chapter 1: Overview and Descriptive Statistics

3 8.

• Number observations equal 2 x 2 x 2 = 8

• This could be called an analytic study because the data would be collected on an existing

process. There is no sampling frame.

9.

• There could be several explanations for the variability of the measurements. Among

them could be measurement error (due to mechanical or technical changes across measurements), recording error, differences in weather conditions at time of measurements, etc.

• No, because there is no sampling frame.

Section 1.2

10.a.

• 9

6 33588

7 00234677889

• 127

9 077 stem: ones

10 7 leaf: tenths

11 368

A representative strength for these beams is around 7.8 MPa, but there is a reasonably large amount of variation around that representative value.

(What constitutes large or small variation usually depends on context, but variation is usually considered large when the range of the data – the difference between the largest and smallest value – is comparable to a representative value. Here, the range is 11.8 – 5.9 = 5.9 MPa, which is similar in size to the representative value of 7.8 MPa. So, most researchers would call this a large amount of variation.)

• The data display is not perfectly symmetric around some middle/representative value.

There is some positive skewness in this data.

• Outliers are data points that appear to be very different from the pack. Looking at the

stem-and-leaf display in part (a), there appear to be no outliers in this data. (A later section gives a more precise definition of what constitutes an outlier.)

• From the stem-and-leaf display in part (a), there are 4 values greater than 10. Therefore,

the proportion of data values that exceed 10 is 4/27 = .148, or, about 15%.

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