What is the difference between between random variation

1. Monitoring the Minting of Half Dollars A half dollar is considered to be defective if it deviates substantially from these specifications: The weight is 11.340 g, the diameter is 30.61 mm, the thickness is 2.15 mm, the composition is 8.33% nickel and 91.67% copper, the edge has 150 reeds, and it is stamped correctly. For the same manufacturing process considered in this section, defects are monitored and the accompanying control chart is obtained. Does this process appear to be within statistical control? If not, identify any out ­of ­control criteria that are violated. Is the manufacturing process deteriorating? ________________ Equation Transcription: Text Transcription: UCL=0.002145 overline{P}=0.001135 LCL=0.000125

Problem 1CQQ What areprocessdata?

Problem 2CQQ What is the difference between between random variation and assignable variation?

Problem 2CRE Workplace Etiquette: ProbabilityBased on the results in Exercise, assume that there is a 0.55 probability of randomly selecting an adult and getting someone who believes that it is inappropriate to wear shorts at work. a.What is the probability of randomly selecting an adult and getting someone who doesnotbelieve that it is inappropriate to wear shorts at work. ________________ b.If five different adults are randomly selected, what is the probability that they all believe that it is inappropriate to wear shorts at work? ________________ c.If five different adults are randomly selected, what is the probability of getting at least one who doesnotbelieve that it is inappropriate to wear shorts at work? Exercise Workplace Etiquette: Confidence IntervalIn a survey conducted by Opinion Research Corporation, randomly selected adults were asked what is inappropriate in the workplace. Among1000responses, 55% said that it is inappropriate to wear shorts. Use the sample results to construct a 95% confidence interval estimate of the proportion of the adult population believing that it is inappropriate to wear shorts at work. Based on the result, does it appear that the majority of adults believe that it is not appropriate to wear shorts at work?

Energy Consumption. Exercises 1–5 refer to the amounts of energy consumed in the author’s home. Each value represents energy consumed (kWh) in a two-month period. Let each subgroup consist of the six amounts within the same year. 2. Energy Consumption: R Chart Let each subgroup consist of the 6 values within a year. Construct an R chart and determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation.

Problem 3BSC Control LimitsIn constructing a control chart for the proportions of defective dimes, it is found that LCL = ?0.000025. What does “LCL” represent, and how should that value be adjusted?

Problem 3CQQ Identify three specific criteria for determining when a process is out of statistical control.

3. Agriculture Experiment: Correlation In 1908, William Gosset published the article “The Probable Error of a Mean” under the pseudonym of “Student” (Biometrika, Vol. 6, No. 1). He included the data listed below for yields from two different types of seed (regular and kiln dried) that were used on adjacent plots of land. The listed values are the yields of straw in cwt per acre, where cwt represents 100 lb. Use a 0.05 significance level to test for a correlation between yields from regular seed and kiln-­dried seed. Are the results useful for addressing the main purpose of the experiment?

Energy Consumption. Exercises 1–5 refer to the amounts of energy consumed in the author’s home. Each value represents energy consumed (kWh) in a two-month period. Let each subgroup consist of the six amounts within the same year. 3. Energy Consumption: \(\mathrm {x\ ^-}\) Chart Let each subgroup consist of the 6 values within a year. Construct an \(\mathrm {x\ ^-}\) chart and determine whether the process mean is within statistical control. If it is not, identify which of the three out­ of ­control criteria lead to rejection of a statistically stable mean. ________________ Equation Transcription: Text Transcription: x ^- x ^-

Problem 4BSC Interpreting a Control ChartAfter constructing a control chart for the proportions of defective dimes, it is concluded that the process is within statistical control. Does that imply that almost all of the dimes meet the desired specifications? Explain.

4. What is the difference between an R chart and an \(\mathrm {x\ ^-}\) chart? ________________ Equation Transcription: Text Transcription: x ^-

Problem 4CRE Agriculture Experiment: Hypothesis TestRefer to the same sample data given in the preceding exercise. Assume that the experiment was conducted to determine whether the new method of using kiln-dried seed is better. Conduct an appropriate hypothesis test.

Energy Consumption. Exercises 1–5 refer to the amounts of energy consumed in the author’s home. Each value represents energy consumed (kWh) in a two-month period. Let each subgroup consist of the six amounts within the same year. 4. Energy Consumption: Run Chart Construct a run chart for the 48 values. Does there appear to be a pattern suggesting that the process is not within statistical control?

Problem 5BSC use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed in Section 14-2 and determine whether the process is within statistical control. If it is not, identify which of the three out-of control criteria apply. Defective DimesConsider a process of minting dimes. Listed below are the numbers of defective dimes in successive batches of 10,000 randomly selected on consecutive days of production. 32 21 25 19 35 34 27 30 26 33

In Exercises 5–8, use the following two control charts that result from testing newly manufactured aircraft altimeters. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 1000 ft. 5. Is the process variation within statistical control? Why or why not? ________________ Equation Transcription: Text Transcription: UCL=111.6 overline{R}=52.8 LCL=0 UCL=26.49 overline{overline{X}}=3.95 LCL=34.40

5. Agriculture Experiment: Descriptive Statistics Using the data given in Exercise 3, find the mean and standard deviation of each of the two samples, then informally compare the results. 3. Agriculture Experiment: Correlation In 1908, William Gosset published the article “The Probable Error of a Mean” under the pseudonym of “Student” (Biometrika, Vol. 6, No. 1). He included the data listed below for yields from two different types of seed (regular and kiln dried) that were used on adjacent plots of land. The listed values are the yields of straw in cwt per acre, where cwt represents 100 lb. Use a 0.05 significance level to test for a correlation between yields from regular seed and kiln­ dried seed. Are the results useful for addressing the main purpose of the experiment?

Energy Consumption. Exercises 1–5 refer to the amounts of energy consumed in the author’s home. Each value represents energy consumed (kWh) in a two-month period. Let each subgroup consist of the six amounts within the same year. 5. Defective Aspirin Tablets The Acton Pharmaceutical Company manufactures aspirin tablets that are supposed to contain 325 mg of aspirin. Each day, 100 tablets are randomly selected and the amount of aspirin is measured. A tablet is considered defective if it has obvious physical deformities or the amount of aspirin is not between 315 mg and 335 mg. The numbers of defects are listed below for consecutive production days. Construct an appropriate control chart and determine whether the process is within statistical control. If not, identify which criteria lead to rejection of statistical stability.

Problem 6BSC use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed in Section 14-2 and determine whether the process is within statistical control. If it is not, identify which of the three out-of control criteria apply. Defective DimesRepeat Exercise assuming that the size of each batch is 100 instead of 10,000. Compare the control chart to the one found for Exercise. Comment on the general quality of the manufacturing process described in Exercise compared to the manufacturing process described in this exercise. Exercise Defective DimesConsider a process of minting dimes. Listed below are the numbers of defective dimes in successive batches of 10,000 randomly selected on consecutive days of production. 32 21 25 19 35 34 27 30 26 33

In Exercises 5–8, use the following two control charts that result from testing newly manufactured aircraft altimeters. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 1000 ft. 6. What is the value of \(\mathrm {R\ ^-}\)? In general, how is a value of \(\mathrm {R\ ^-}\) obtained? ________________ Equation Transcription: Text Transcription: UCL=111.6 overline{R}=52.8 LCL=0 UCL=26.49 overline{overline{X}}=3.95 LCL=34.40 R ^- R ^-

Problem 6CRE Defective Child Restraint SystemsThe Tracolyte Manufacturing Company produces plastic frames used for child booster seats in cars. During each week of production, 50 frames are selected and tested for conformance to all regulations by the Department of Transportation. Frames are considered defective if they do not meet all requirements. Listed below are the numbers of defective frames among the 50 that are tested each week. Use a control chart forpto verify that the process is within statistical control. If it is not in control, explain why it is not. 4 5 5 3 6 5 7 7 9 10

Problem 7BSC use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed in Section 14-2 and determine whether the process is within statistical control. If it is not, identify which of the three out-of control criteria apply. Birth RateIn recent and consecutive years, 100,000 people were randomly selected and the numbers of births they generated were found, with the results given below. (The listed values are based on data from theCIA World Factbook, and they are the most recent values available at the time of this writing.) 1422 1410 1414 1415 1413 1414 1414 1416 1418 1382 1383 1383

In Exercises 5–8, use the following two control charts that result from testing newly manufactured aircraft altimeters. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 1000 ft. 7. Is the process mean within statistical control? Why or why not? ________________ Equation Transcription: Text Transcription: UCL=111.6 overline{R}=52.8 LCL=0 UCL=26.49 overline{overline{X}}=3.95 LCL=34.40

Problem 7CRE Overtime Football Games: GraphThe overtime rule for football became effective in 1974. Since then, 3.8% of overtime games have ended in a tie, 25.6% ended with a touchdown, 70.1% ended with a field goal, and 0.5% ended with a safety. Construct a graph that is effective in displaying these results.

Problem 8BSC use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed in Section 14-2 and determine whether the process is within statistical control. If it is not, identify which of the three out-of control criteria apply. Violent CrimesIn each of recent and consecutive years, 100,000 people in the United States were randomly selected and the number who were victims of violent crime was determined, with the results listed below. Does the rate of violent crime appear to exhibit acceptable behavior? (The values are based on data from the U.S. Department of Justice, and they are the most recent values available at the time of this writing.) How does the result affect us? 685 637 611 566 523 507 505 494 476 463 469 474 467 458 429

In Exercises 5–8, use the following two control charts that result from testing newly manufactured aircraft altimeters. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 1000 ft 8. What is the value of \(\mathrm {x\ ^{-\ -}}\)? In general, how is a value of \(\mathrm {x\ ^{-\ -}}\) found? ________________ Equation Transcription: Text Transcription: UCL=111.6 overline{R}=52.8 LCL=0 UCL=26.49 overline{overline{X}}=3.95 LCL=34.40 x ^{- -} x ^{- -}

Problem 8CRE Designing Motorcycle HelmetsEngineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 15.2 cm and a standard deviation of 2.5 cm (based on anthropometric survey data from Gordon, Churchill, et al). a.What percentage of men have head breadths greater than 17 cm? If helmets are made to accommodate only males with head breadths less than 17 cm, would those helmets exclude too many males? ________________ b.If, due to financial constraints, the helmets are designed to fit all men except those with head breadths that are in the smallest 5% or largest 5%, find the minimum and maximum head breadths that the helmets will fit.

Problem 9BSC use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed in Section 14-2 and determine whether the process is within statistical control. If it is not, identify which of the three out-of control criteria apply. Voting RateIn each of recent and consecutive years of presidential elections, 1000 people of voting age in the United States were randomly selected and the number who voted was determined, with the results listed below. (The data are the latest available as of this writing.) Comment on the voting behavior of the population. 631 619 608 552 536 526 531 501 551 491 513 553 568

Problem 9CQQ What is apchart?

Problem 9CRE SamplingWhat is the difference between a voluntary response sample and a simple random sample? Which is generally better for the use of statistical methods?

Problem 10BSC use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed in Section 14-2 and determine whether the process is within statistical control. If it is not, identify which of the three out-of control criteria apply. College Enrollment by High School GraduatesIn each of several recent and consecutive years, 1000 high school graduates were randomly selected and the numbers who enrolled in college were recorded (based on data from theStatistical Abstract of the United States).The data are the latest available as of this writing. Does the process appear to be pro-ceding as it should? 626 619 619 650 670 656 629 633 618 652 639 672 686 660 672 690 693 681

10. Examine the following p chart for defective car batteries and briefly describe the action that should be taken. ________________ Equation Transcription: Text Transcription: UCL=0.12338 overline{P}=0.0858 LCL=0.04822

Problem 10CRE StatisticsWhich of the following is the singlemostimportant factor for obtaining good results from a statistical study? a.Size of the sample b.Importance of the topic being addressed c.Sampling method d.Using data at the ratio level of measurement e.Using graphs that are not misleading

Problem 11BSC use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed in Section 14-2 and determine whether the process is within statistical control. If it is not, identify which of the three out-of control criteria apply. Cola CansIn each of several consecutive days of production of cola cans, 500 cans are tested and the numbers of defects each day are listed below. What action should be taken? 20 22 19 17 19 15 16 13 14 14 11 13 12 11 10 9 9 10 7 7

Problem 12BSC use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed in Section 14-2 and determine whether the process is within statistical control. If it is not, identify which of the three out-of control criteria apply. Smart Phone BatteriesThe SmartBatt company manufactures batteries for smart phones. Listed below are numbers of defects in batches of 200 randomly selected in each of 15 consecutive days of production. What action should be taken? 12 11 14 15 9 10 12 16 8 9 15 7 17 5 18

13. np Chart A variation of the control chart for p is the np chart in which the actual numbers of defects are plotted instead of the proportions of defects. The np chart has a centerline value of \(\mathrm {n\ p\ ^{-}}\), and the control limits have values of \(\mathrm {n\ p\ ^{-}+3\ n\ p\ ^-\ q\ ^-}\) and \(\mathrm {n\ p\ ^{-}-3\ n\ p\ ^-\ q\ ^-}\). The p chart and the np chart differ only in the scale of values used for the vertical axis. Construct the np chart for Example 1 in this section. Compare the np chart to the control chart for p given in this section. ________________ Equation Transcription: Text Transcription: n p ^{-} n p ^{-}+3 n p ^{-} q ^{-} n p ^{-}-3 n p ^{-} q ^{-}