Concept explainers
According to the article “Fatigue Testing of Condoms” (Polymer Testing, 2009: 567–571), “tests currently used for condoms are surrogates for the challenges they face in use,” including a test for holes, an inflation test, a package seal test, and tests of dimensions and lubricant quality (all fertile territory for the use of statistical methodology!). The investigators developed a new test that adds cyclic strain to a level well below breakage and determines the number of cycles to break. A sample of 20 condoms of one particular type resulted in a sample mean number of 1584 and a sample standard deviation of 607. Calculate and interpret a confidence interval at the 99% confidence level for the true average number of cycles to break. [Note: The article presented the results of hypothesis tests based on the t distribution; the validity of these depends on assuming
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Chapter 7 Solutions
Probability and Statistics for Engineering and the Sciences
- Cheek teeth of extinct primates. The characteristics of cheek teeth (e.g., molars) can provide anthropologists with information on the dietary habits of extinct mammals. The cheek teeth of an extinct primate species were the subject of research reported in the American Journal of Physical Anthropology (Vol. 142, 2010). A total of 18 cheek teeth extracted from skulls discovered in western Wyoming were analyzed. Researchers recorded the dentary depth of molars (in millimeters) for a sample of 18 cheek teeth extracted from skulls. These depth measurements are listed in the accompanying table. Anthropologists know that the mean dentary depth of molars in an extinct primate species— called Species A—is 15 millimeters. Is there evidence to indicate that the sample of 18 cheek teeth come from some other extinct primate species (i.e., some species other than Species A)? The data are given below (you will need to put it into a single column). You will need to calculate the sample…arrow_forwardThe authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement" compared two different instruments for measuring a subject's ability to breathe out air.† (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen subjects participated in the study, and for each subject air flow was measured once using the Wright meter and once using the mini-Wright meter. Subject 1 2 3 4 5 6 7 8 9 Mini- Wright Meter 512 430 520 428 500 600 364 380 658 Wright Meter + 494 395 516 434 476 557 413 442 650 Subject 10 11 12 13 14 15 16 17 Mini- Wright Meter 445 432 626 260 477 259 350 451 Wright Meter 433 417 656 267 478 178 423 427 (a) Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce different readings but there is…arrow_forwardThe authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement" compared two different instruments for measuring a subject's ability to breathe out air.† (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen subjects participated in the study, and for each subject air flow was measured once using the Wright meter and once using the mini-Wright meter. Subject Mini-WrightMeter WrightMeter Subject Mini-WrightMeter WrightMeter 1 512 494 10 445 433 2 430 395 11 432 417 3 520 516 12 626 656 4 428 434 13 260 267 5 500 476 14 477 478 6 600 557 15 259 178 7 364 413 16 350 423 8 380 442 17 451 427 9 658 650 (a) Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce…arrow_forward
- The authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement" compared two different instruments for measuring a subject's ability to breathe out air.† (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen subjects participated in the study, and for each subject air flow was measured once using the Wright meter and once using the mini-Wright meter. Subject Mini-WrightMeter WrightMeter Subject Mini-WrightMeter WrightMeter 1 512 494 10 445 433 2 430 395 11 432 417 3 520 516 12 626 656 4 428 434 13 260 267 5 500 476 14 477 478 6 600 557 15 259 178 7 364 413 16 350 423 8 380 442 17 451 427 9 658 650 (a) Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce different readings but there is a…arrow_forwardThe authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement" compared two different instruments for measuring a subject's ability to breathe out air.+ (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen subjects participated in the study, and for each subject air flow was measured once using the Wright meter and once using the mini-Wright meter. Mini- Subject Wright Meter 1 2 3 4 5 6 7 8 9 512 430 520 428 500 600 364 380 658 Wright Meter 494 395 516 434 476 557 413 442 650 Subject 10 11 12 13 14 15 16 17 Mini- Wright Meter 445 432 626 260 477 259 350 451 Wright Meter 433 417 656 267 478 178 423 427 (a) Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce different readings but there is a…arrow_forwardYou may need to use the appropriate appendix table or technology to answer this question. An agency reports that 11.7% of workers in a particular country belonged to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership. (a) Formulate the hypotheses that can be used to determine whether union membership has increased. H0: p = 0.117 Ha: p ≠ 0.117 H0: p ≥ 0.117 Ha: p < 0.117 H0: p ≤ 0.117 Ha: p > 0.117 H0: p < 0.117 Ha: p ≥ 0.117 H0: p > 0.117 Ha: p ≤ 0.117 (b) If the sample results show that 42 of the workers belonged to unions, what is the p-value for your hypothesis test? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value =arrow_forward
- You may need to use the appropriate appendix table or technology to answer this question. An agency reports that historically 11.3% of workers in a particular country belong to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership. (a) Formulate the hypotheses that can be used to determine whether union membership has increased. H0: p ≥ 0.113 Ha: p < 0.113 H0: p = 0.113 Ha: p ≠ 0.113 H0: p ≤ 0.113 Ha: p > 0.113 H0: p < 0.113 Ha: p ≥ 0.113 H0: p > 0.113 Ha: p ≤ 0.113 (b) If the sample results show that 36 of the workers belonged to unions, what is the p-value for your hypothesis test? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = (c) At α = 0.05, what is your conclusion? Reject H0. There is insufficient evidence to conclude that there has been an increase in union…arrow_forwardYou may need to use the appropriate appendix table or technology to answer this question. An agency reports that 11.5% of workers in a particular country belonged to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership. (a) Formulate the hypotheses that can be used to determine whether union membership has increased. H0: p ≥ 0.115 Ha: p < 0.115 H0: p ≤ 0.115 Ha: p > 0.115 H0: p = 0.115 Ha: p ≠ 0.115 H0: p > 0.115 Ha: p ≤ 0.115 H0: p < 0.115 Ha: p ≥ 0.115 (b) If the sample results show that 36 of the workers belonged to unions, what is the p-value for your hypothesis test? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = (c) At ? = 0.05, what is your conclusion? Reject H0. There is insufficient evidence to conclude that there has been an increase in union…arrow_forwardYou are the quality control manager of a water bottles company. One of the biggest complaints in the past years has been the breakage and, hence, the concern on the durability of the connector between the lid and the bottle which many users use as a handle for the bottles. To collect evidence before implementing any modification to the production process, your department has subjected 50 water bottles to a durability test and the following data on the number of times the handles have been used to lift the bottles before they break. 2- 1495 1499 1502 1500 1491 1498 1498 1495 1488 1516 1513 1486 1504 1503 1493 1504 1489 1500 1495 1499 1501 1507 1511 1496 1486 1497 1510 1504 1493 1482 1511 1502 1520 1514 1486 1514 1500 1505 1512 1500 1504 1498 1503 1514 1474 1489 1488 1506 1517 1490 Assume that the number of times the handles have been used to lift the bottles before they break follows a normal distribution. You want to test to see if there is enough evidence that the mean number of times…arrow_forward
- Does buttered toast fall face down? Data was collected to test this. 40 slices of toast (each with butter on one side) were dropped (from the same height). 24 slices (60%) landed buttered side down. We would like to use the results of this study to determine if there is statistical evidence that toast tends to land buttered side down more than 50% of the time.arrow_forwardRegulations from the Environmental Protection Agency say that soil used in play areas should not have lead levels that exceed a 400 parts per million (ppm). Before beginning construction at a new site, an agent will take a sample of soil and run a significance test on the mean lead level in the soil. If the mean lead level in the sample is significantly higher than 400 ppm, then the soil is deemed unsafe and construction cannot continue. Here are the hypotheses for this test: Ho : µ 400 ppm (soil is unsafe) (where u is the mean lead level in the soil at the new site). Which of the following would be a Type I error in this setting? Choose 1 answer: The soil is actually safe, and the sample result is below 400 ppm. so construction continues. The soil is actually safe, and the sample result is significantly higher than 400 ppm. so construction stops. The soil is actually unsafe, and the sample result is below 400 ppm, so construction continues. The soil is actually unsafe, and the sample…arrow_forwardRegulations from the Environmental Protection Agency say that soil used in play areas should not have lead levels that exceed a 400 parts per million (ppm). Before beginning construction at a new site, an agent will take a sample of soil and run a significance test on the mean lead level in the soil. If the mean lead level in the sample is significantly higher than 400 ppm, then the soil is deemed unsafe and construction cannot continue. Here are the hypotheses for this test: Ho : µ 400 ppm (soil is unsafe) (where u is the mean lead level in the soil at the new site). Which of the following would be a Type I error in this setting?arrow_forward
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