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Probability And Statistics For Engineers And Scientists 3rd Edition Anthony Hayter - Solutions

Eight samples of a polymer compound were obtained and their densities were measured as given in DS 8.5.2.(a) Use an appropriate hypothesis lest to assess whether there is sufficient evidence to establish that the average density of these kind of compounds is larger than 3.50.(b) Construct a 99%
In a sample of size 33 a sample mean of 382.97 and a sample standard deviation of 3.81 are obtained. (a) Use an appropriate hypothesis test to assess whether there is sufficient evidence to establish that the population mean is different from 385. (b) Construct a 999? two-sided confidence interval
Show how Table III can be used to put bounds on the /'-values for these hypothesis tests. (a) n = 24. x- = 2.39. s = 0.21. H0: μ = 2.5. HA : μ ≠ 2.5 (b) n = 30. x- = 0.538, s = 0.026, H0: μ > 0.540, HA : μ < 0.540 (c) n = 10, x- = 143.6, s = 4.8, H0 : μ < 135.0, HA:μ > 135.0 You can use the
A paper company sells paper that is supposed to* have a weight of 75.0 g/m2. In a quality inspection, the weights of 30 random samples of paper are measured. The sample mean of these weights is x- = 74.63 g/nr. with a sample standard deviation of s = 2.095 g/m2.(a) Is there any evidence that the
A group of medical researchers is investigating how artery disease affects the rigidity of the arteries. Deformity measurements are made on a sample of 14 diseased arteries, and a sample mean of x- = 0.497 is obtained, with a sample standard deviation of s = 0.0764. (a) What is the evidence that
Consider the data set of osteoporosis patient heights given in DS 6.6.4. Use a computer package to construct 90%, 95%, and 99% two-sided t-intervals for the mean height. Is 70 inches a plausible value for the mean height?
Consider the data set in DS 6.6.5 of bamboo shoot heights 40 days after planting. Use a computer package to construct 90%, 95%, and 99% two-sided /-intervals for the mean shoot height. A previous study reported that under similar growing conditions the mean shoot height after 40 days was more than
The breaking strengths of a random sample of 26 molded plastic housings ere measured, and a sample mean of x- = 479.42 and a sample standard deviation of s = 12.55 were obtained. A confidence interval (472.56. 486.28) for the average strength of molded plastic housings was constructed from these
Composites are materials that are made by embedding a fiber, such as glass or carbon, inside a matrix, such as a metal or a ceramic. Composites are used in civil engineering structures, and their degradation when subjected to weather conditions is an important issue. In an experiment to investigate
Recall the data set of soil compressibility measurements given in DS 6.6.6. Construct a 9995 one-sided confidence interval that provides an upper bound on the average soil compressibility. Can the engineers conclude that the average soil compressibility is no larger than 25.5?
Shows the data obtained from a paired experiment performed to examine which of two assembly methods is quicker on average. A random sample of 35 workers on an assembly line were selected and all were timed while they assembled an item in the standard manner (method A) and while they assembled an
Researchers into the genetic disease sickle cell anemia are interested in how red blood cells adhere to endothelial cells, which form the innermost lining of blood vessels. A set of 14 blood samples are obtained, and each sample is split in half. One half of the blood sample is profused over an
An experiment is performed to assess whether a new tire wears more slowly than a standard tire. A set of 20 trucks is chosen. A new tire is placed on one of the front wheels of each truck, and a standard tire is placed on the other front wheel. Right and left positions of the two kinds of tire are
A new teaching method for a calculus class is being evaluated. A set of 80 students is formed into 40 pairs, where the two-pair members have roughly equal mathematics test scores. The pairs are then randomly split. With one member being assigned to section A where the standard teaching method is
Two independently operated laboratories provide historical dating services using radioactive carbon dating methods. A researcher suspects that one laboratory tends to provide older datings than the other laboratory. To investigate this supposition 18 samples of old material are split in half. One
A sports manufacturer has developed a new golf ball with special dimples that it hopes will cause the ball to travel farther than standard golf balls. This question is examined by asking 24 golfers to hit 10 new balls and 10 standard balls. Each ball is hit off a tee. and randomization techniques
An experiment was conducted to compare two procedures (A and B) for measuring a person's reaction time to a stimulus. Ten volunteers participated in the experiment, and each volunteer was given the stimulus twice. For each person the reaction time was measured once with procedure A and once with
Eight cultures of a bacterium are split in half. One half is tested using a standard antibiotic and the other half is tested using a new antibiotic. The data values in DS '.1.2.8 are the times taken to kill the bacterium. Use an appropriate hypothesis test to assess whether there is any evidence
An experiment is conducted to investigate how the addition of a surfactant affects the ability of magnetized steel wool to remove uranium-oxide particles from water. Six batches of uranium-oxide contaminated water are obtained that are each split in half, and the surfactant is added to one of the
In an unpaired two-sample problem, an experimenter observes n = 38, = 5.782 from population A and m = 40, = 6.443 from population B. Suppose that the experimenter wishes to use values σA = σB = 2.0 for the population standard deviations. (a) What is the exact p-value for the hypothesis testing
The resilient moduli of n = 10 samples of a clay mixture of type A are measured and the sample mean is = 19.50. In addition, the resilient moduli of m = 12 samples of a clay mixture of type B are measured and the sample mean is = 18.64. Suppose that the experimenter wishes to use values σA =
An experimenter feels that observations from population A have a standard deviation no larger than 10.0 and that observations from population B have a standard deviation no larger than 15.0. If the experimenter wants a two-sided 99% confidence interval for the difference in population means with a
An experimenter would like to construct a two-sided 95% confidence interval for the difference between the average resistance of two types of copper cable with a length no larger than L0 = 1.0 ohms. If the experimenter feels that the standard deviations of the resistances of either type of cable
Consider again the data set in Problem 9.3.2 with sample sizes n = m = 14. If a two-sided 99% confidence interval for the difference in population means is required with a length no larger than L0 = 5.0, what additional sample sizes would you recommend be obtained from the two populations?
Consider again the data set of glass sheet thicknesses in Problem 9.3.6 with sample sizes n = m = 41. If a two-sided 99% confidence interval for the difference in the average thickness of glass sheets produced by the two processes is required with a length no larger than L0 = 0.1 mm, how many
An experiment was conducted to investigate how the corrosion properties of chilled cast iron depend upon the chromium content of the alloy. A collection of n = 12 samples of chilled cast iron with 0.1% chromium content provided corrosion rates with a sample mean of = 2.462 and a sample standard
Recall that DS 6.1.7 shows the weights of a sample of paving slabs from a certain company, manufacturer A say. In addition. DS 9.3.1 shows the weights of a sample of paving slabs from another company, manufacturer B. Is there evidence of any difference in the paving slab weights between the two
An engineer compares the sample of paint thicknesses in DS 6.1.8 from production line A with a sample of paint thicknesses in DS 9.3.2 from production line B. What conclusions should the engineer draw?
In an unpaired two-sample problem an experimenter observes n = 14, x = 32.45, sx = 4.30 from population A and n = 14, = 32.45, sx = 4.30 from population B. A and m = 14, = 41.45, sy = 5.23 from population B. (a) Use the pooled variance method to construct a 99% two-sided confidence interval for
In the garment industry, bleaching is an important component of the manufacturing process. Chlorine bleach is very effective, but it can be unsatisfactory for environmental reasons. Consequently, various alternative bleaches such as hydrogen peroxide have been investigated. DS 9.3.4 contains the
The breaking strengths of 14 randomly selected objects produced from a standard procedure had a mean of 56.43 and a standard deviation of 6.30. In addition, the breaking strengths of 20 randomly selected objects produced from a new procedure had a mean of 62.11 and a standard deviation of 7.15.
A simple clinical trial was performed to compare two medicines. A total of 20 patients were obtained, and they were randomly split into two groups of 10 patients each. One group received medicine A. and the other group received medicine B. The patients' responses are given in DS 9.3.6. Does this
She had 8 times recorded when she ran in the morning and these had a sample average of 132.52 minutes with a Standard deviation of 1.31 minutes. In addition, she had 10 times recorded when she ran in the afternoon and these had a sample average of 133.87 minutes with a standard deviation of 1.72
A random sample of 10 observations from population A has a sample mean of 152.30 and a sample standard deviation of 1.83. A random sample of 8 observations from population B has a sample standard deviation of 1.04. If the p-value for the one-sided hypothesis test with an alternative hypothesis HA:
In an unpaired two-sample problem an experimenter observes n = 8, = 675.1, sx = 44.76 from population A and m = 17, = 702.4, sy = 38.94 from population B. (a) Use the pooled variance method to construct a 99% two-sided confidence interval for μA - μB. (b) Construct a 9995 two-sided confidence
In an unpaired two-sample problem an experimenter observes n = 10. = 7.76. sx = 1.07 from population A and m = 9, = 6.88. Sy = 0.62 from population B. (a) Construct a 99% one-sided confidence interval μA - μB ∈ (c, ∞) without assuming equal population variances. (b) Does the value of c
In an unpaired two-sample problem an experimenter observes n = 13. = 0.0548, sx = 0.00128 from population A and m = 15, = 0.0569, sy = 0.00096 from population B. (a) Construct a 95% one-sided confidence interval μA - μB ∈ (-∞, c) using the pooled variance method. (b) Consider a one-sided
The thicknesses of n = 41 glass sheets made using process A are measured and the statistics = 3.04 mm and sx = 0.124 mm are obtained. In addition, the thicknesses of m = 41 glass sheets made using process B are measured and the statistics = 3.12 mm and sy = 0.137 mm are obtained. Use a pooled
The breaking strengths of n = 20 bundles of wool fibers have a sample mean = 436.5 and a sample standard deviation sx = 11.90. In addition, the breaking strengths of m = 25 bundles of synthetic fibers have a sample mean = 452.8 and a sample standard deviation sy = 4.61. Answer the following
A random sample of n = 16 one-kilogram sugar packets of brand A have weights with a sample mean = 1.053 kg and a sample standard deviation sx = 0.058 kg. In addition, a random sample of m = 16 one-kilogram sugar packets of brand B have weights with a sample mean = 1.071 kg and a sample standard
In an unpaired two-sample problem, an experimenter observes n = 47, = 100.85 from population A and m = 62, = 89.32 from population B. Suppose that the experimenter wishes to use values σA = 25 and σB = 20 for the population standard deviations. (a) What is the exact p-value for the hypothesis
A researcher is interested in how a color video display rather than a black-and-white video display can help a person assimilate the information provided on a screen. A set of 22 experimental subjects are used, and each person undergoes five trials with a color display and five trials with a
A sample of n = 18 observations from population A has a sample standard deviation of sx = 6.48, and a sample of m = 21 observations from population B has a sample standard deviation of sy = 9.62. Obtain a 909": confidence interval for the ratio of the population variances.
Consider again the data set of glass sheet thicknesses in Problem 9.3.6 with sample sizes n = m = 41. Construct a 90% confidence interval for the ratio of the variances of the thicknesses of glass sheets produced by the two processes.
Consider again the data set of the breaking strengths of n = 20 bundles of wool fibers and m = 25 bundles of synthetic fibers in Problem 9.3.7. Construct 90%, 95%, and 997r confidence intervals for the ratio of the variances of the breaking strengths of the two types of liber.
The strengths of two types of canvas were compared in an experiment. Fourteen samples of type A gave an average Strength of 327,433 with a standard deviation of 9.832. Twelve samples of type B gave an average strength of 335.537 with a standard deviation of 10,463. Use a hypothesis test to evaluate
The strengths of nine reinforced cement samples were tested using two procedures. Each sample was split into two parts, with one part being tested with procedure 1 and the other part being tested with procedure 2. The resulting data set is given in DS 9.6.7. Use an appropriate hypothesis test to
Are the following statements true or false? (a) The advantage of paired experiments is that am carry-over effects from one treatment to the other treatment do not affect the analysis. (b) In an experiment to compare two treatments with an independent samples design, the random allocation of the
Eight people participated in an experiment to compare two experimental drug therapies. Each person was administered both therapies, but in a random order. The data values given in DS 9.6.8 were obtained. Perform a hypothesis test to investigate whether there is any evidence of a difference between
A sample of 20 items from manufacturer A were measured and a sample mean of 2376.3 and a sample standard deviation of 24.1 were obtained. Also, a sample of 24 items from manufacturer B were measured and a sample mean of 2402.0 and a sample standard deviation of 26.4 were obtained. (a) Use a
In assessing how the water absorption properties of cotton fabric differ with roller pressures of 10 pounds per square inch and 20 pounds per square inch, an experimenter suspects that different fabric samples may have different absorption properties. Therefore a paired experimental design is
Patients with spinal cord injuries can lose mobility in their arms and hands, and it is important to find the optimal design of a joystick that will enable them to perform tasks in the most efficient manner. An experiment was designed to compare two joystick designs. As a target moved across a
A researcher in the petroleum industry is interested in the sizes of wax crystals produced when wax dissolved in a supercritical fluid is sprayed through a capillary nozzle. In the first experiment, a pre-expansion temperature of 80°C is employed and the diameters of n = 35 crystals are measured
A company is investigating how long it takes its drivers to deliver goods from its factory to a nearby port for export. Records reveal that with a standard specified driving route, the last n = 48 delivery times have a sample mean of = 432.7 minutes and a sample standard deviation of sx = 20.39
In a quality drive a food manufacturer reorganizes its consumer complaints division. Before the reorganization, a study was conducted of the time that a consumer calling the toll-free complaints line had to wait before speaking to a company employee. After reorganization, a similar follow-up study
The viscosity of oil after it has been used in an engine over a period of time may change from its initial value because the high temperature inside the engine can cause the oil to break down. An experiment was conducted to compare the effect on oil viscosity of two different engines. Various
Suppose that x = 11 is an observation from a B(32, p) random variable. (a) Compute a two-sided 99% confidence interval for p. (b) Compute a two-sided 95% confidence interval for p. (c) Compute a one-sided 99% confidence interval that provides an upper bound for p. (d) Consider the hypotheses H0: p
Suppose that you wish to find a population proportion p with accuracy ±2% with 99% confidence. What sample size n would you recommend if p could be 0.5? What if the population proportion p can be assumed to be no larger than 0.40?
In experimental bioengineering trials, a successful outcome was achieved 73 times out of 120 attempts. Construct a 99% two-sided confidence interval for the probability of a success under these conditions. If this probability is required to be known to a precision of ±5%. how many additional
A manufacturer receives a shipment of 100.000 computer chips. A random sample of 200 chips is examined, and 8 of these are found to be defective. Construct a 95% confidence level upper bound on the total number of defective chips in the shipment.
A glass tube is designed to withstand a pressure differential of 1.1 atmospheres. In testing, it was found that 12 out of 20 tubes could in fact withstand a pressure differential of 1.5 atmospheres. Calculate a two-sided 95% confidence interval for the probability that a tube can withstand a
An audit of a federal assistance program implemented after a major regional disaster discovered that out of 85 randomly selected applications. 17 contained errors due to either applicant fraud or processing mistakes. If there were 7607 applications made to the federal assistance program, calculate
A city councilor asks your advice on how many householders should be polled in order to gauge the support for a tax increase to build more schools. The councilor wants to assess the support to within ±5% with 95% confidence. What sample size would you recommend if the councilor advises you that
In a particular day, 22 out of 542 visitors to a website followed a link provided by one of the advertisers. Calculate a 99'- two-sided confidence interval for the probability that a user of the website will follow a link provided by an advertiser.
The dielectric breakdown strength of an electrical insulator is defined to be the voltage at which the insulator starts to leak detectable amounts of electrical current, and it is an important safety consideration. In an experiment. 62 insulators of a certain type were tested at 180°C. and it was
Out of a random sample of 210 parts produced on a production line, 31 fail a quality inspection. Obtain a 99% two-sided confidence interval for the proportion of parts from the production line that will fail the quality inspection.
Suppose that x = 21 is an observation from a B(27, p) random variable. (a) Compute a two-sided 99% confidence interval for p. (b) Compute a two-sided 95% confidence interval for p. (c) Compute a one-sided 95'; confidence interval that provides a lower bound for p. (d) Consider the hypotheses H0: p
A random sample of 38 wheelchair users were asked whether they preferred cushion type A or B. and 28 of them preferred type A whereas only 10 of them preferred type B. Use a hypothesis test to assess whether it is fair to conclude that cushion type A is at least twice as popular as cushion type B.
A newspaper reported the results of a political poll about which candidate likely voters preferred, together with a note that the margin of error was plus or minus 3.5 percentage points and that the numbers were based on answers from 793 likely voters. How was this margin of error calculated? Do
A random-number generator is supposed to produce a sequence of Os and I s with each value being equally likely to be a 0 or a I and with all values being independent. In an examination of the random-number generator, a sequence of 50.000 values is obtained of which 25.264 are Os. (a) Formulate a
A new radar system is being developed to detect packages dropped by airplane. In a series of trials, the radar detected the packages being dropped 35 times out of 44. Construct a 95% lower confidence bound on the probability that the radar successfully detects dropped packages.
Two experiments are performed. In the first experiment a six-sided die is rolled 50 times and a 0 is scored twice. In the second experiment the die is rolled 100 times and a 0 is scored four times. Which of the two experiments provides the most support for the claim that the die has been weighted
If 21 6s are obtained from 100 rolls of a die. should the null hypothesis that the probability of scoring a 6 is 1/6 be rejected at the size α = 0.05 level?
A court holds jurisdiction over live counties, and the juries are required to be made up in a representative manner from the eligible populations of these five counties. An investigator notices that the county where she lives has 14% of the total population of the five counties eligible for jury
In trials of a medical screening test for a particular illness. 23 cases out of 324 positive results turned out to be "false-positive" results. The screening test is acceptable as long as p, the probability of a positive result being incorrect, is no larger than 10%. Calculate a p-value for the
Suppose that you wish to find a population proportion p with accuracy ± I % with 95% confidence. What sample size n would you recommend if p could be 0.5? What if the population proportion p can be assumed to be larger than 0.75?
Suppose that x = 14 is an observation from a B(37, pA) random variable, and that y = 7 is an observation from a B(26. pB) random variable. (a) Compute a two-sided 99% confidence interval for PA - PB. (b) Compute a two-sided 95% confidence interval for PA - PB. (c) Compute a one-sided 99% confidence
An audit of a federal assistance program implemented after a major regional disaster discovered that out of 85 randomly selected applications processed during the first two weeks after the disaster. 17 contained errors due to either applicant fraud or processing mistakes. However, out of 132
Two scanning machines are compared. When 185 items were scanned with machine A. 159 of the the scans were free of errors. When the same 185 items were scanned with machine B, only 138 of the scans were free of errors. Is this sufficient evidence to conclude that in general the probability of an
Recall from Problem 10.1.16 that in a particular day, 22 out of 542 visitors to a website followed a link provided by an advertiser. After the advertisements were modified, it was found that 64 out of 601 visitors to the website on a day followed the link. Is there any evidence that the
Consider again Problem 10.1.18 where 62 insulators of a certain type were tested at 180 C. and it was found that 13 had a dielectric breakdown strength below a specified threshold level. In addition. 70 insulators of the same type were tested at 250 C, and it was found that 20 had a dielectric
A group of 250 patients was randomly split into two groups of 125 patients. The lirst group of 125 patients was given treatment A. and 72 of them improved their condition. The second group of 125 patients was given treatment B, and 60 of them improved their condition. Perform a hypothesis test to
A company is performing a failure analysis for two of its products. It found that for the first product 76 out of 243 failures were due to operator misuse, while for the second product 122 out of 320 failures were due to operator misuse. Construct a 99% two-sided Confidence interval for the
Suppose that x = 261 is an observation from a B(302, pA) random variable, and that y = 401 is an observation from a B(454, pB) random variable. (a) Compute a two-sided 99% confidence interval for PA - PB (b) Compute a two-sided 90% confidence interval for PA - PB (c) Compute a one-sided 95%
Suppose that the abilities of two new radar systems to detect packages dropped by airplane are being compared. In a series of trials, radar system A detected the packages being dropped 35 times out of 44, while radar system B detected the packages being dropped 36 times out of 52. (a) Construct a
Die A is rolled 50 times and a 6 is scored 4 times, while a 6 is obtained 10 times when die B is rolled 50 times. (a) Construct a two-sided 99% confidence interval for the difference in the probabilities of scoring a 6 on the two dice. (b) Calculate a p-value for the two-sided null hypothesis that
In an experiment to determine the best conditions to produce suitable crystals for the recovery and purification of biological molecules such as enzymes and proteins, crystals had appeared within 24 hours in 27 out of 60 trials of a particular solution without seed crystals, and had appeared within
A new drug is being compared with a standard drug for treating a particular illness. In the clinical trials, a group of 200 patients was randomly split into two groups, with one group being given the standard drug and one group the new drug. Altogether S3 out of the 100 patients given the new drug
A company has two production lines for constructing television sets. Over a certain period of time. 23 out of I I28 television sets from production line A are found not to meet the company's quality standards, while 24 out of 962 television sets from production line B are found not to meet the
In experimental bioengineering trials, a successful outcome was achieved 73 times out of 120 attempts using a standard procedure, whereas with a new procedure a successful outcome was achieved 101 times out of 120. What is the evidence that the new procedure is better than the standard procedure?
A manufacturing company has to choose between two potential suppliers of computer chips. A random sample of 200 chips from supplier A is examined and 8 are found to be defective, while 13 chips out of a random sample of 250 chips from supplier B are found to be defective. Use two-sided inference
DS 10.3.1 gives the results of n = 500 die rolls. (a) What are the expected cell frequencies if the die is a fair one? (b) Calculate the Pearson chi-square statistic X2 for testing whether the die is fair. (c) Calculate the likelihood ratio chi-square statistic G2 for testing whether the die is
In a biological experiment a large quantity of plants were grown. For each plant the stem length was classified as being either tall or dwarf, and the position of the flowers was classified as being either axial or terminal. All together there were 412 tall axial plants. 121 tall terminal plants.
Each of 205 consumers was asked to choose which of three products they preferred. Product A was chosen hv S3 of the consumers, product B was chosen by 75 of the consumers, and product C was chosen by 47 of the consumers. Is there sufficient evidence to conclude that the three products do not have
The acidity of a chemical solution can be classified as "very high." '•high." 'normal." "low," and "very low." A total of 630 samples of the solution from a production process were obtained, and the acidities were classified as given in DS 10.3.13. (a) Perform a two-sided hypothesis test of the
An experiment was performed to investigate how long batteries remain charged under certain storage conditions. A total of 125 batteries were charged to the same level and stored in the designated conditions. After 24 hours all 125 batteries were tested and it was found that 12 of them had charges
The data set in DS 10.3.14 shows the number of shark attacks along a popular stretch of coastline for each of the past 76 years. Is it plausible that the number of shark attacks per year follows a Poisson distribution with mean 2.5?
DS 10.3.2 presents a data set on the number of rolls of a die required before a 6 is obtained. If the probability of scoring a 0 is 1/6. then the distribution of the number of rolls required until a 6 is scored is a geometric distribution with parameter p = 1/6. Test whether this distribution is
A garage sells tires of types A. B, and C, and the owner surmises that a customer is twice as likely to choose type A as type B, and twice as likely to choose type B as type C. (a) Is this supposition plausible based upon the data set in DS 10.3.3 of this year's sales? (b) Calculate a 99% two-sided
A court has jurisdiction over five counties, ami of the people eligible for jury duty. 14% reside in county A. 22% reside in county B. 35% reside in county C, 16% reside in county D, and 13% reside in county E. DS 10.3.4 gives the residential locations of the jurors selected over a five-year

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