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Engineering Statistics 5th edition

November 01, 2010

Chapter 1 1-1

a) One choice for the outcome variable is the proportion of students that complete a degree within a specified time period, such as six years after starting the program. In addition to the number of years until the degree is completed the final grade point average could also be used as a response. b) Predictor variables can include high school grade point average, either overall or in selected courses such as math and science, and scores on standardized exams. Information about whether students were full-time or worked while in college or were involved in co-op programs could be used as candidate predictors. Similarly, information about student involvement in extracurricular activities (sports, clubs, etc) may be relevant. Academic performance in certain university level courses (such as mathematics, science and engineering science) may be useful predictors. c) The data for such a study should be available from student records, including exit interviews with graduating students. Since the data is collected on students graduating from the program this is a retrospective study.

1-5

a) Because the study results will be applied more generally to a larger population of dental patients this is a conceptual population. b) The random division is used to avoid a systematic difference between the patients in the two groups. For example, one would not want all younger patients in one group sand older patients in another because any difference in groups might be due the fluoride, but might also be due to the age difference. Consequently, the age effect would be confused (the term confounded is used) with the fluoride effect. Similarly any other pattern between the patients in the two groups would be a cause for concern of confounding. Therefore, the random assignment is used to avoid such systematic differences. c) No the study would not be valid. Patients with more concern for tooth care, who more consistently clean their teeth, may select the fluoride group. As in the previous part, then the tooth cleaning effect would be confounded with the fluoride treatment. d) It is possible that a single group generates little or no tooth decay. One would not want to attribute this result to the use of fluoride without a comparison. For example, if the control group also generated little or no tooth decay then the effects of fluoride are not demonstrated. One would need the control group to generate more tooth decay than the fluoride group to demonstrate the positive effects of fluoride on tooth decay.

1-7

The sample is not random. All the samples are selected from the same hour of the day. It is possible that production during this hour is unusual relative to the other times.

1-9

a) The number of samples of size two is 4 choose 2 = 4!/(2!2!) = 6 b) One could list all six subsets of size 2 as {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d} and randomly select one of these six subsets. An alternative approach is to randomly select one member at random from {a,b,c,d} and then randomly select another member from the remaining three. Both approaches can be used to select a random sample of size two.

1-11

The conclusion is not correct. The 6% defective in the sample is based on only 50 bearings and the true proportion defective may be greater than or less than 6%. Later chapters in the book will discuss how to quantify the uncertainty in sample data.

1-13

It is not reasonable to consider these measurements a random sample of bolts because only one bolt is measured multiple times. Variations in the production of bolts are not accounted for in these measurements. If the analysis is to focus on only the single bolt then one might consider these measurements a random sample from the populations of all measurements of this single bolt.