New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
mathematics
statistics

Introduction To Statistical Quality Control 7th Edition Douglas C Montgomery - Solutions

The following are the rankings given by three judges to the works of 10 artists:Calculate the value of W, the coefficient of concordance of Exercise 16.15, as a measure of the agreement of the three sets of rankings.
With reference to Exercise 16.42, calculate the k = 3 pairwise rank correlation coefficients and verify that the relationship between their mean S and the coefficient of concordance (see Exercise 16.15) is given byIn exercise
The following are the miles per gallon obtained with 40 tankfuls of a certain kind of gasoline:Assuming that the underlying conditions are met, use the sign test at the 0.01 level of significance to test the null hypothesis = 24.2 against the alternative hypothesis > 24.2.
Rework Exercise 16.44 using the signed- rank test.In exerciseThe following are the miles per gallon obtained with 40 tankfuls of a certain kind of gasoline:Assuming that the underlying conditions are met, use the sign test at the 0.01 level of significance to test the null hypothesis = 24.2
The following are the numbers of passengers carried on flights 136 and 137 between Chicago and Phoenix on 12 days:Use the sign test at the 0.01 level of significance to test the null hypothesis µ1 = µ2 (that on the average the two flights carry equally many passengers) against the alter-native
Rework Exercise 16.46 using the signed- rank test based on Table X.In exerciseThe following are the numbers of passengers carried on flights 136 and 137 between Chicago and Phoenix on 12 days:Use the sign test at the 0.01 level of significance to test the null hypothesis µ1 = µ2 (that on the
The following are the numbers of employees absent from two government agencies on 25 days: 24 and 29, 32 and 45, 36 and 36, 33 and 39, 41 and 48, 45 and 36, 33 and 41, 38 and 39, 46 and 40, 32 and 39, 37 and 30, 34 and 45, 41 and 42, 32 and 40, 30 and 33, 46 and 42, 38 and 50, 34 and 37, 45 and 39,
Rework Exercise 16.48 using the signed- rank test based on Table X. In exercise The following are the numbers of employees absent from two government agencies on 25 days: 24 and 29, 32 and 45, 36 and 36, 33 and 39, 41 and 48, 45 and 36, 33 and 41, 38 and 39, 46 and 40, 32 and 39, 37 and 30, 34 and
Show that (a) U1 + U2 = n1n2 for any pair of values of the corresponding random variables; (b) The random variables corresponding to U1 and U2 both take on values on the range from 0 to n1n2.
A sample of 24 suitcases carried by an airline on transoceanic flights weighed 32.0, 46.4, 48.1, 27.7, 35.5, 52.6, 66.0, 41.3, 49.9, 36.1, 50.0, 44.7, 48.2, 36.9, 40.8, 35.1, 63.3, 42.5, 52.4, 40.9, 38.6, 43.2, 41.7, and 35.6 pounds. Test at the 0.05 level of significance whether the mean weight of
The following is a random sample of the I.Q.€™s of husbands and wives: 108 and 103, 104 and 116, 103 and 106, 112 and 104, 99 and 99, 105 and 94, 102 and 110, 112 and 128, 119 and 106, 106 and 103, 125 and 120, 96 and 98, 107 and 117, 115 and 130, 101 and 100, 110 and 101, 103 and 96, 105 and
An examination designed to measure basic knowledge of American history was given to random samples of freshmen at two major universities, and their grades wereUse the U test at the 0.05 level of significance to test the null hypothesis that there is no difference in the average knowledge of
The following are data on the breaking strength (in pounds) of random samples of two kinds of 2-inch cotton ribbons:Use the U test at the 0.05 level of significance to test the claim that Type I ribbon is, on the average, stronger than Type II ribbon.
To compare four bowling balls, a professional bowler bowls five games with each ball and gets the following results:Use the Kruskal-Wallis test at the 0.05 level of significance to test whether the bowler can expect to score equally well with the four bowling balls.
The following are the miles per gallon that a test driver got for 10 tankfuls of each of three kinds of gasoline:Use the Kruskal-Wallis test at the 0.05 level of significance to test whether there is a difference in the actual average mileage yield of the three kinds of gasoline.
Three groups of guinea pigs were injected, respectively, with 0.5, 1.0, and 1.5 milligrams of a tranquilizer, and the following are the numbers of seconds it took them to fall asleep:Use the H test at the 0.01 level of significance to test the null hypothesis that the differences in dosage have no
The following are the numbers of defective pieces produced by a machine on 50 consecutive days: 7, 14, 17, 10, 18, 19, 23, 19, 14, 10, 12, 18, 19, 13, 24, 26, 9, 16, 19, 14, 19, 10, 15, 22, 25, 24, 20, 9, 17, 28, 29, 19, 25, 23, 24, 28, 31, 19, 24, 30, 27, 24, 39, 35, 23, 26, 28, 31, 37, and 40.
The following are the numbers of lunches that an insurance agent claimed as business deductions in 30 consecutive months: 6, 7, 5, 6, 8, 6, 8, 6, 6, 4, 3, 2, 4, 4, 3, 4, 7, 5, 6, 8, 6, 6, 3, 4, 2, 5, 4, 4, 3, and 7. Use the runs test based on Table XII to test for randomness at the 0.01 level of
The numbers of retail stores that opened for business and also quit business in the same year were 108, 103, 109, 107, 125, 142, 147, 122, 116, 153, 144, 162, 143, 126, 145, 129, 134, 137, 143, 150, 148, 152, 125, 106, 112, 139, 132, 122, 138, 148, 155, 146, and 158 during a period of 33 years.
Show that the distribution of the random variable corresponding to W1 is symmetrical aboutAnd hence that the distribution of the random variable corresponding to U1 is symmetrical about n1n2/2.
Verify that U1 and U2 are also given byAnd
If X1, X2, . . ., Xn1 and Y1, Y2, . . ., Yn2 are independent random samples, we can test the null hypothesis that they come from identical continuous populations on the basis of the Mann-Whitney statistic U, which is simply the number of pairs (xi, yj) for which xi > yj. Symbolically,Where For i =
Verify that the Kruskal-Wallis statistic on page 464 is equivalent to
Suppose that during the analyze phase an obvious solution is discovered. Should that solution be immediately implemented and the remaining steps of DMAIC abandoned? Discuss your answer.
Construct a normal probability plot of the chemical process yield data in Exercise 3.9. Does the assumption that process yield is well modeled by a normal distribution seem reasonable?
Consider the viscosity data in Exercise 3.10. Construct a normal probability plot, a lognormal probability plot, and a Weibull probability plot for these data. Based on the plots, which distribution seems to be the best model for the viscosity data?
Table 3E.4 contains 20 observations on cycles to failure of aluminum test coupons subjected to repeated alternating stress of 15,000 psi at 20 cycles per second. Construct a normal probability plot, a lognormal probability plot, and a Weibull probability plot for these data. Based on the plots,
Consider the outpatient service times in Exercise 3.3. Construct a normal probability plot, an exponential probability plot, and a Weibull probability plot for these data. Do any of these distributions seem to be a reasonable probability model for the data? Based on the plots, which distribution is
Consider the call handling times in Exercise 3.4. Construct a normal probability plot, an exponential probability plot, and a gamma probability plot for these data. Do any of these distributions seem to be a reasonable probability model for the data? Based on the plots, which distribution is the
The bore diameters of eight randomly selected bearings are shown here (in mm): 50.001, 50.002, 49.998, 50.006, 50.005, 49.996, 50.003, 50.004(a) Calculate the sample average.(b) Calculate the sample standard deviation.
Consider the concentration of suspended solids from Exercise 3.17. Assume that reading across, then down, gives the data in time order. Construct and interpret a time-series plot.
Consider the chemical process yield data in Exercise 3.9. Calculate the sample average and standard deviation.
Suppose that two fair dice are tossed and the random variable observed—say, x—is the sum of the two up faces. Describe the sample space of this experiment, and determine the probability distribution of x.
Find the mean and variance of the random variable in Exercise 3.27.
A mechatronic assembly is subjected to a final functional test. Suppose that defects occur at random in these assemblies, and that defects occur according to a Poisson distribution with parameter λ = 0.02.(a) What is the probability that an assembly will have exactly one defect?(b) What is the
The service time in minutes from admit to discharge for ten patients seeking care in a hospital emergency department are 21, 136, 185, 156, 3, 16, 48, 28, 100, and 12. Calculate the mean and standard deviation of the service time.
The probability distribution of x is f(x) = ke–x,0 ≤ x ≤ . Find the appropriate value of k. Find the mean and variance of x.
The random variable x takes on the values 1, 2, or 3 with probabilities (1 + 3k)/3, (1 + 2k)/3, and (0.5 + 5k)/3, respectively.(a) Find the appropriate value of k. (b) Find the mean and variance of x. (c) Find the cumulative distribution function.
The probability distribution of the discrete random variable x is p(x) = krx, 0 < r < 1. Find the appropriate value for k if x = 0, 1, ...
A manufacturer of electronic calculators offers a one-year warranty. If the calculator fails for any reason during this period, it is replaced. The time to failure is well modeled by the following probability distribution: A manufacturer of electronic calculators offers a one-year warranty. If the
The net contents in ounces of canned soup is a random variable with probability distribution Find the probability that a can contains less than 12 ounces of product.
A production process operates with 1% nonconforming output. Every hour a sample of 25 units of product is taken, and the number of nonconforming units counted. If one or more nonconforming units are found, the process is stopped and the quality control technician must search for the cause of
A random sample of 50 units is drawn from a production process every half hour. The fraction of nonconforming product manufactured is 0.02. What is the probability that be p ≤ 0.04 if the fraction nonconforming really is 0.02?
A sample of 100 units is selected from a production process that is 1% nonconforming. What is the probability that pˆ will exceed the true fraction nonconforming by k standard deviations, where k = 1, 2, and 3?
Suppose that 10% of the adult population has blood chemistry parameters consistent with a diagnosis of a pre-diabetic condition. Of four volunteer participants in a health screening study, what is the probability that one of them is pre-diabetic?
The Really Cool Clothing Company sells its products through a telephone ordering process. Since business is good, the company is interested in studying the way that sales agents interact with their customers. Calls are randomly selected and recorded, then reviewed with the sales agent to identify
Patients arriving at an outpatient clinic are routinely screened for high blood pressure. Assume that this condition occurs in 15% of the population. These are Bernoulli trials, with constant probability of success p = 0.15 on each trial, where success is finding a patient with high blood
A stock brokerage has four computers that are used for making trades on the New York Stock Exchange. The probability that a computer fails on any single day is 0.005. Failures occur independently. Any failed computers are repaired after the exchange closes, so each day can be considered an
A computer system uses passwords consisting of the lowercase letters (a–z) and the integers (0–9). There are 10,000 users with unique passwords. A hacker randomly selects (with replacement) passwords in an attempt to break into the system. (a) Suppose that 8000 of the users have six-character
An electronic component for a medical X-ray unit is produced in lots of size N = 25. An acceptance testing procedure is used by the purchaser to protect against lots that contain too many nonconforming components. The procedure consists of selecting five components at random from the lot (without
A lot of size N = 30 contains three nonconforming units. What is the probability that a sample of five units selected at random contains exactly one nonconforming unit? What is the probability that it contains one or more nonconformances?
A textbook has 500 pages on which typographical errors could occur. Suppose that there are exactly 10 such errors randomly located on those pages. Find the probability that a random selection of 50 pages will contain no errors. Find the probability that 50 randomly selected pages will contain at
Surface-finish defects in a small electric appliance occur at random with a mean rate of 0.1 defects per unit. Find the probability that a randomly selected unit will contain at least one surface-finish defect.
Glass bottles are formed by pouring molten glass into a mold. The molten glass is prepared in a furnace lined with firebrick. As the firebrick wears, small pieces of brick are mixed into the molten glass and finally appear as defects (called “stones”) in the bottle. If we can assume that stones
The billing department of a major credit card company attempts to control errors (clerical, data transmission, etc.) on customers’ bills. Suppose that errors occur according to a Poisson distribution with parameter λ = 0.01. What is the probability that a customer’s bill selected at random
A production process operates in one of two states: the in-control state, in which most of the units produced conform to specifications, and an out-of-control state, in which most of the units produced are defective. The process will shift from the in-control to the out-of-control state at random.
An inspector is looking for nonconforming welds in the gasoline pipeline between Phoenix and Tucson. The probability that any particular weld will be defective is 0.01. The inspector is determined to keep working until finding three defective welds. If the welds are located 100 feet apart, what is
Reconsider the power supply manufacturing process in Exercise 3.52. Suppose we wanted to improve the process. Can shifting the mean reduce the number of nonconforming units produced? How much would the process variability need to be reduced in order to have all but one out of 1000 units conform to
If x is normally distributed with mean  and standard deviation , and given that the probability that x is less than 32 is 0.0228, find the value of .
A lightbulb has a normally distributed light output with mean 5000 end foot-candles and standard deviation of 50 end foot-candles. Find a lower specification limit such that only 0.5% of the bulbs will not exceed this limit.
A quality characteristic of a product is normally distributed with mean µ and standard deviation . Specifications on the characteristic are 6 x 8. A unit that falls within specifications on this quality characteristic results in a profit of C0. However, if x < 6 the profit is
Consider the furnace temperature data in Exercise 3.5. (a) Find the sample median of these data. (b) How much could the largest temperature measurement increase without changing the sample median?
Derive the mean and variance of the Poisson distribution.
Derive the mean and variance of the exponential distribution.
Derive the mean and variance of the geometric distribution.
The data shown in Table 3E.2 are chemical process yield readings on successive days (read down, then across). Construct a histogram for these data. Comment on the shape of the histogram. Does it resemble any of the distributions that we have discussed in this chapter?
Suppose that you are testing the following hypotheses where the variance is known:H0: μ =100 H1: μ ≠ 100Find the P-value for the following values of the test statistic.(a) Z0 = 2.75(b) Z0= 1.86(c) Z0= −2.05(d) Z0= −1.86
Using the data from Exercise 4.7, construct a 95% lower confidence interval on mean battery life. Why would the manufacturer be interested in a one-sided confidence interval?
A new process has been developed for applying photoresist to 125-mm silicon wafers used in manufacturing integrated circuits. Ten wafers were tested, and the following photoresist thickness measurements (in angstromx × 1000) were observed: 13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918,
A machine is used to fill containers with a liquid product. Fill volume can be assumed to be normally distributed. A random sample of ten containers is selected, and the net contents (oz) are as follows: 12.03, 12.01, 12.04, 12.02, 12.05, 11.98, 11.96, 12.02, 12.05, and 11.99.(a) Suppose that the
Ferric chloride is used as a flux in some types of extraction metallurgy processes. This material is shipped in containers, and the container weight varies. It is important to obtain an accurate estimate of mean container weight. Suppose that from long experience a reliable value for the standard
The diameters of aluminum alloy rods produced on an extrusion machine are known to have a standard deviation of 0.0001 in. A random sample of 25 rods has an average diameter of 0.5046 in.(a) Test the hypothesis that mean rod diameter is 0.5025 in. Assume a two-sided alternative and use =
Two machines are used for filling glass bottles with a soft-drink beverage. The filling processes have known standard deviations 1 = 0.010 liter and 2 = 0.015 liter, respectively. A random sample of n1 = 25 bottles from machine 1 and n2 = 20 bottles from machine 2 results in average net
Two quality control technicians measured the surface finish of a metal part, obtaining the data in Table 4E.1. Assume that the measurements are normally distributed.(a)Test the hypothesis that the mean surface finish measurements made by the two technicians are equal. Use a = 0.05 and assume equal
Suppose that x1 ~ N(1, 12) and x2 ~ N(2, 22), and that x1 and x2 are independent. Develop a procedure for constructing a 100(1 − )% confidence interval on 1 − 2, assuming that 12 and 22 are unknown and cannot be assumed equal.
(a) Test the hypothesis that the mean hardness for the saltwater quenching process equals the mean hardness for the oil quenching process. Use a = 0.05 and assume equal variances.Test H0: 1 2 = 0 vs. H1: 1 2 0. Reject H0 if |t0|>t/2, n1+n2-2.(b) Assuming that the
Suppose that you are testing the following hypotheses where the variance is known: H0 :  100 H1 :  100 Find the P-value for the following values of the test statistic. (a) Z0 = 2.50 (b) Z0 = 1.95 (c) Z0 = 2.05 (d) Z0 = 2.36
A random sample of 200 printed circuit boards contains 18 defective or nonconforming units. Estimate the process fraction nonconforming.(a) Test the hypothesis that the true fraction nonconforming in this process is 0.10. Use a = 0.05. Find the P-value.(b) Construct a 90% two-sided confidence
A random sample of 500 connecting rod pins contains 65 nonconforming units. Estimate the process fraction nonconforming.(a) Test the hypothesis that the true fraction defective in this process is 0.08. (b) Find the P-value for this test.
Two processes are used to produce forgings used in an aircraft wing assembly. Of 200 forgings selected from process 1, 10 do not conform to the strength specifications, whereas of 300 forgings selected from process 2, 20 are nonconforming.
A new purification unit is installed in a chemical process. Before its installation, a random sample yielded the following data about the percentage of impurity: x12  9.85,s12  6.79 and n1 10 . After installation, a random sample resulted in x22  8.08,s22  6.18 and n2  8. (a) Can
Two different types of glass bottles are suitable for use by a soft-drink beverage bottler. The internal pressure strength of the bottle is an important quality characteristic. It is known that 1 = 2 = 3.0 psi. From a random sample of n1 = n2 = 16 bottles, the mean pressure strengths are
The diameter of a metal rod is measured by 12 inspectors, each using both a micrometer caliper and a vernier caliper. The results are shown in Table 4E.3. Is there a difference between the mean measurements produced by the two types of caliper? Use ï¡ = 0.01.
The cooling system in a nuclear submarine consists of an assembly pipe through which a coolant is circulated. Specifications require that weld strength must meet or exceed 150 psi.(a) Suppose the designers decide to test the hypothesis H0:  = 150 versus H1:  > 150. Explain why this choice
An experiment was conducted to investigate the filling capability of packaging equipment at a winery in Newberg, Oregon. Twenty bottles of Pinot Gris were randomly selected and the fill volume (in ml) measured. Assume that fill volume has a normal distribution. The data are as follows: 753, 751,
Suppose we wish to test the hypotheses H0 :  15H1 :   15where we know that 2 = 9.0. If the true mean is really 20, what sample size must be used to ensure that the probability of type II error is no greater than 0.10? Assume that  = 0.05.What n is needed such that the Type II
Consider the hypothesesH0 :   0H1 :   0where 2 is known. Derive a general expression for determining the sample size for detecting a true mean of 1  0 with probability 1 −  if the type I error is .
Suppose that you are testing the following hypotheses where the variance is known: H0 :  100 H1 :  100 Find the P-value for the following values of the test statistic. (a) Z0 = −2.35 (b) Z0 = −1.99 (c) Z0 = −2.18 (d) Z0 = −1.85
Suppose we are testing the hypothesesH0 : 1  2H1 : 1  2where 12 and 22 are known. Resources are limited, and consequently the total sample size n1 + n2 = N. How should we allocate the N observations between the two populations to obtain the most powerful test?
There is a typographical error in the hypotheses (should be 22) in early printings of the 7th edition; this solution is for the correct hypotheses.Develop a test for the hypothesesH0 : 1  22H1 : 1  22where 12 and 22 are known.
Nonconformities occur in glass bottles according to a Poisson distribution . A random sample of 100 bottles contains a total of 11 nonconformities.(a) Develop a procedure for testing the hypothesis that the mean of a Poisson distribution equals a specified value 0. (b) Use the results of part
An inspector counts the surface-finish defects in dishwashers. A random sample of five dishwashers contains three such defects. Is there reason to conclude that the mean occurrence rate of surface-finish defects per dishwasher exceeds 0.5? Use the results of part (a) of Exercise 4.32 and assume
An in-line tester is used to evaluate the electrical function of printed circuit boards. This machine counts the number of defects observed on each board. A random sample of 1,000 boards contains a total of 688 defects. Is it reasonable to conclude that the mean occurrence rate of defects is  =
An article in Solid State Technology (May 1987) describes an experiment to determine the effect of C2F6 flow rate on etch uniformity on a silicon wafer used in integrated-circuit manufacturing. Three flow rates are tested, and the resulting uniformity (in percent) is observed for six test units at
Compare the mean etch uniformity values at each of the C2F6 flow rates from Exercise 4.33 with a scaled t distribution. Does this analysis indicate that there are differences in mean etch uniformity at the different flow rates? Which flows produce different results?
Compare the mean compressive strength at each rodding level from Exercise 4.37 with a scaled t distribution. What conclusions would you draw from this plot?
An aluminum producer manufactures carbon anodes and bakes them in a ring furnace prior to use in the smelting operation. The baked density of the anode is an important quality characteristic, as it may affect anode life. One of the process engineers suspects that firing temperature in the ring
Suppose that you are testing the following hypotheses where the variance is unknown: H0 :  100H1 :   100The sample size is n = 20. Find bounds on the P-value for the following values of the test statistic.(a) t0 = 2.75(b) t0 = 1.86(c) t0 = −2.05(d) t0 = −1.86
Plot the residuals from Exercise 4.36 against the firing temperatures. Is there any indication that variability in baked anode density depends on the firing temperature? What firing temperature would you recommend using?
An article in Environmental International describes an experiment in which the amount of radon released in showers was investigated. Radon-enriched water was used in the experiment, and six different orifice diameters were tested in showerheads. The data from the experiment are shown in Table

Showing 40200 - 40300 of 88243

First
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
Last

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved