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Chapter 8: Q2E (page 458)
What are the treatments for a designed experiment with two factors, one qualitative with two levels (A and B) and one quantitative with five levels (50, 60, 70, 80, and 90)?
There are ten treatments (A,50), (A,60), (A,70), (A,80), (A,90), (B,50), (B,60), (B,70), (B,80), (B,90).
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Estimating production time.A widely used technique for estimating the length of time it takes workers to produce a product is the time study. In a time study, the task to be studied is divided into measurable parts, and each is timed with a stopwatch or filmed for later analysis. For each worker, this process is repeated many times for each subtask. Then the average and standard deviation of the time required to complete each subtask are computed for each worker. A worker鈥檚 overall time to complete the task under study is then determined by adding his or her subtask-time averages (Gaither and Frazier, Operations Management, 2001). The data (in minutes) given in the table are the result of a time study of a production operation involving two subtasks.
| Worker A | Worker B | |||
Repetition | Subtask 1 | Subtask 2 | Subtask 1 | Subtask 2 |
1 | 30 | 2 | 31 | 7 |
2 | 28 | 4 | 30 | 2 |
3 | 31 | 3 | 32 | 6 |
4 | 38 | 3 | 30 | 5 |
5 | 25 | 2 | 29 | 4 |
6 | 29 | 4 | 30 | 1 |
7 | 30 | 3 | 31 | 4 |
a.Find the overall time it took each worker to complete the manufacturing operation under study.
b.For each worker, find the standard deviation of the seven times for subtask 1.
c.In the context of this problem, what are the standard deviations you computed in part bmeasuring?
d.Repeat part b for subtask 2.
e.If you could choose workers similar to A or workers similar to B to perform subtasks 1 and 2, which type would you assign to each subtask? Explain your decisions on the basis of your answers to parts a鈥揹.
4.111 Personnel dexterity tests. Personnel tests are designed to test a job applicant鈥檚 cognitive and/or physical abilities. The Wonderlic IQ test is an example of the former; the Purdue Pegboard speed test involving the arrangement of pegs on a peg board is an example of the latter. A particular
dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 75 and standard deviation 7.5.
a. A particular employer requires job candidates to score at least 80 on the dexterity test. Approximately what percentage of the test scores during the past year exceeded 80?
b. The testing service reported to a particular employer that one of its job candidate鈥檚 scores fell at the 98th percentile of the distribution (i.e., approximately 98% of the scores were lower than the candidate鈥檚, and only 2%were higher). What was the candidate鈥檚 score?
Non-destructive evaluation. Non-destructive evaluation(NDE) describes methods that quantitatively characterize materials, tissues, and structures by non-invasive means, such as X-ray computed tomography, ultrasonic, and acoustic emission. Recently, NDE was used to detect defects in steel castings (JOM,May 2005). Assume that the probability that NDE detects a 鈥渉it鈥� (i.e., predicts a defect in a steel casting) when, in fact, a defect exists is .97. (This is often called the probability of detection.) Also assume that the probability that NDE detects a hit when, in fact, no defect exists is .005. (This is called the probability of a false call.) Past experience has shown a defect occurs once in every 100 steel castings. If NDE detects a hit for a particular steel casting, what is the probability that an actual defect exists?
Consider the discrete probability distribution shown here.
x | 10 | 12 | 18 | 20 |
p | .2 | .3 | .1 | .4 |
a. Calculate and .
b. What is ?
c. Calculate .
d. What is the probability that xis in the interval ?
To compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results:
Sample 1 | Sample 2 |
a. Use a confidence interval to estimate the difference between the population means . Interpret the confidence interval.
b. Test the null hypothesis versus the alternative hypothesis . Give the significance level of the test and interpret the result.
c. Suppose the test in part b was conducted with the alternative hypothesis . How would your answer to part b change?
d. Test the null hypothesis versus . Give the significance level and interpret the result. Compare your answer with the test conducted in part b.
e. What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a鈥揹?
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