Probability And Statistics For Engineering And The Sciences 8th Ed

Test Bank For Probability And Statistics For Engineering And The Sciences 8th Ed by Jay L. Devore. Chapter 1 – Overview and Descriptive Statistics SHORT ANSWER 1. Give one possible sample of size 4 from each of the following populations: a. All daily newspapers published in the United States b. All companies listed on the New York Stock Exchange c. All students at your college or university d. All grade point averages of students at your college or university ANS: a. Houston Chronicle, Des Moines Register, Chicago Tribune, Washington Post b. Capital One, Campbell Soup, Merrill Lynch, Pulitzer c. John Anderson, Emily Black, Bill Carter, Kay Davis d. 2.58. 2.96, 3.51, 3.69 PTS: 1 2. A Southern State University system consists of 23 campuses. An administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. Describe and discuss several different sampling methods that might be employed. Would this be an enumerative or an analytic study? Explain your reasoning. ANS: 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 from 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. PTS: 1 3. A Michigan city divides naturally into ten district neighborhoods. How might a real estate appraiser select a sample of single-family homes that could be used as a basis for developing an equation to predict appraised value from characteristics such as age, size, number of bathrooms, and distance to the nearest school, and so on? Is the study enumerative or analytic? ANS: 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 homes in the sample the necessary variables would be collected. This would be an enumerative study because there exists a finite, identifiable population of objects from which to sample. PTS: 1 4. An experiment was carried out to study how flow rate through a solenoid valve in an automobile’s pollution-control system depended on three factors: armature lengths, spring load, and bobbin depth. Two different levels (low and high) of each factor were chosen, and a single observation on flow was made for each combination of levels. a. The resulting data set consisted of how many observations? b. Is this an enumerative or analytic study? Explain your reasoning. ANS: a. Number observations equal 2 2 2=8 b. This could be called an analytic study because the data would be collected on an existing process. There is no sampling frame. PTS: 1 5. The accompanying data specific gravity values for various wood types used in construction . .41 .41 .42 .42. .42 .42 .42 .43 .44 .54 .55 .58 .62 .66 .66 .67 .68 .75 .31 .35 .36 .36 .37 .38 .40 .40 .40 .45 .46 .46 .47 .48 .48 .48 .51 .54 Construct a stem-and-leaf display using repeated stems and comment on any interesting features of the display. ANS: One method of denoting the pairs of stems having equal values is to denote the stem by L, for ‘low’ and the second stem by H, for ‘high’. Using this notation, the stem-and-leaf display would appear as follows: 3L 1 stem: tenths 3H 56678 leaf: hundredths 4L 234 5L 144 5H 58 6L 2 6H 6678 7L 7H 5 The stem-and-leaf display on the previous page shows that .45 is a good representative value for the data. In addition, the display is not symmetric and appears to be positively skewed. The spread of the data is .75 - .31 = .44, which is .44/.45 = .978 or about 98% of the typical value of .45. This constitutes a reasonably large amount of variation in the data. The data value .75 is a possible outlier. PTS: 1 6. Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data: 0 4 2 1 3 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1 2 1 2 4 0 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3 5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3 a. Determine frequencies and relative frequencies for the observed values of x = number of nonconforming transducers in a batch. b. What proportion of batches in the sample has at most four nonconforming transducers? What proportion has fewer than four? What proportion has at least four nonconforming units? ANS: a. Number Nonconforming Frequency Relative Frequency 0 7 0.117 1 12 0.200 2 13 0.217 3 14 0.233