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statistical sampling to auditing

Principles Of Statistics For Engineers And Scientists 2nd International Edition William Navidi - Solutions

Fill in the blank: For observed and expected values, i. the row totals in the observed table must be the same as the row totals in the expected table, but the column totals need not be the same.ii. the column totals in the observed table must be the same as the column totals in the expected table,
For the given table of observed values:a. Construct the corresponding table of expected values.b. If appropriate, perform the chi-square test for the null hypothesis that the row and column outcomes are independent. If not appropriate, explain why.Observed Values 123 A 25 4 11 B 33 4 C 42 3 5
For the given table of observed values:a. Construct the corresponding table of expected values.b. If appropriate, perform the chi-square test for the null hypothesis that the row and column outcomes are independent. If not appropriate, explain why.Observed Values 123 A 15 10 12 B 3 11 11 C 9 14 12
The article “The Effectiveness of Child Restraint Systems for Children Aged 3 Years or Younger During Motor Vehicle Collisions: 1996 to 2005” (T.Rice and C. Anderson, American Journal of Public Health, 2009:252–257) studied a large number of automobile accidents involving small children.
The article “Chronic Beryllium Disease and Sensitization at a Beryllium Processing Facility” (K. Rosenman, V. Hertzberg, et al., Environmental Health Perspectives, 2005:1366–1372) discusses the effects of exposure to beryllium in a cohort of workers. Workers were categorized by their duration
The article “Analysis of Time Headways on Urban Roads: Case Study from Riyadh” (A. Al-Ghamdi, Journal of Transportation Engineering, 2001:289–294) presents a model for the time elapsed between the arrival of consecutive vehicles on urban roads. Following are 137 arrival times (in
The article “Inconsistent Health Perceptions for US Women and Men with Diabetes” (M. McCollum, L. Hansen, et al., Journal of Women’s Health, 2007:1421–1428) presents results of a survey of adults with diabetes. Each respondent was categorized by gender and income level. The numbers in each
At an assembly plant for light trucks, routine monitoring of the quality of welds yields the following data:Number of Welds High Moderate Low Quality Quality Quality Total Day Shift 467 191 42 700 Evening Shift 445 171 34 650 Night Shift 254 129 17 400 Total 1166 491 93 1750 Can you conclude that
Fasteners are manufactured for an application involving aircraft. Each fastener is categorized as conforming (suitable for its intended use), downgraded(unsuitable for its intended use but usable for another purpose), or scrap (not usable). It is thought that 85% of the fasteners are conforming,
The following MINITAB output presents the results of a hypothesis test for a population mean ????. Some of the numbers are missing. Fill them in.One-Sample T: X Test of mu = 16 vs not = 16 Variable N Mean StDev SE Mean 95% CI T P X 11 13.2874 (a) 1.8389 ((b), (c)) (d) 0.171
The following MINITAB output presents the results of a hypothesis test for a population mean ????.One-Sample T: X Test of mu = 5.5 vs > 5.5 95%Lower Variable N Mean StDev SE Mean Bound T P X 5 5.92563 0.15755 0.07046 5.77542 6.04 0.002a. Is this a one-tailed or two-tailed test?b. What is the null
The article “Approximate Methods for Estimating Hysteretic Energy Demand on Plan-Asymmetric Buildings” (M. Rathhore, A. Chowdhury, and S.Ghosh, Journal of Earthquake Engineering, 2011:99–123) presents a method, based on a modal pushover analysis, of estimating the hysteretic energy demand
The article “Arsenic and Mercury in Lake Whitefish and Burbot Near the Abandoned Giant Mine on Great Slave Lake” (P. Cott, B. Zajdlik, et al., Journal of Great Lakes Research, 2016:223–232) presents measurements of arsenic concentrations in fish found in Northern Canada. In a sample of 8
Eight specimens of Incoloy 825 steel were immersed in acidified brine for four hours. The number of corrosive pits was counted on each sample. The results were 11 26 34 21 42 18 31 34 Can you conclude that the mean number of pits that develop under these conditions is less than 40?
The article “Solid-Phase Chemical Fractionation of Selected Trace Metals in Some Northern Kentucky Soils” (A. Karathanasis and J. Pils, Soil and Sediment Contamination, 2005:293–308) reports that in a sample of 26 soil specimens taken in a region of northern Kentucky, the average
Specifications call for the wall thickness of two-liter polycarbonate bottles to average 4.0 mils. A quality control engineer samples 7 two-liter polycarbonate bottles from a large batch and measures the wall thickness (in mils) in each. The results are 3.999, 4.037, 4.116, 4.063, 3.969, 3.955, and
The thicknesses of six pads designed for use in aircraft engine mounts were measured. The results, in mm, were 40.93, 41.11, 41.47, 40.96, 40.80, and 41.32.a. Can you conclude that the mean thickness is greater than 41 mm?b. Can you conclude that the mean thickness is less than 41.4 mm?c. The
The article “Influence of Penetration Rate on Penetrometer Resistance” (G. Gagnon and J. Doubrough, Canadian Journal of Civil Engineering, 2011:741–750) describes a study in which twenty 2-L specimens of water were drawn from a public works building in Bridgewater, Nova Scotia. The mean lead
A new process for producing a type of novolac resin is supposed to have a mean cycle time of 3.5 hours per batch. Six batches are produced, and their cycle times, in hours, were 3.45 3.47 3.57 3.52 3.40 3.63 Can you conclude that the mean cycle time is greater than 3.5 hours?
Suppose you have purchased a filling machine for candy bags that is supposed to fill each bag with 16 oz of candy. Assume that the weights of filled bags are approximately normally distributed. A random sample of 10 bags yields the following data (in oz):15.87 16.02 15.78 15.83 15.69 15.81 16.04
A geologist is making repeated measurements (in grams) on the mass of a rock. It is not known whether the measurements are a random sample from an approximately normal population. Following are three sets of replicate measurements, listed in the order they were made. For each set of readings, state
Each of the following hypothetical data sets represents some repeated measurements on the concentration of carbon monoxide (CO) in a gas sample whose CO concentration is known to be 60 ppm. Assume that the readings are a random sample from a population that follows the normal curve. Perform a t
The following MINITAB output presents the results of a hypothesis test for a population proportion p. Some of the numbers are missing. Fill them in.Test and CI for One Proportion: X Test of p = 0.7 vs p < 0.7 95%Upper Variable X N Sample p Bound Z-Value P-Value X 345 500 (a) 0.724021 (b) (c)
The following MINITAB output presents the results of a hypothesis test for a population proportion p.Test and CI for One Proportion: X Test of p = 0.4 vs p < 0.4 95%Upper Variable X N Sample p Bound Z-Value P-Value X 73 240 0.304167 0.353013 −3.03 0.001a. Is this a one-tailed or two-tailed
The General Social Survey asked a sample of 1294 people whether they performed any volunteer work during the past year. A total of 517 people said they did. Can you conclude that more than 35% of adults performed volunteer work during the past year?
A sociologist sampled 200 people who work in computer-related jobs and found that 42 of them have changed jobs in the past six months. Can you conclude that more than 15% of computer-related workers have changed jobs in the past six months?
Let A and B represent two variants (alleles) of the DNA at a certain locus on the genome. Assume that 40% of all the alleles in a certain population are type A and 30% are type B. The locus is said to be in Hardy–Weinberg equilibrium if the proportion of organisms that are of type AB is
A grinding machine will be qualified for a particular task if it can be shown to produce less than 8% defective parts. In a random sample of 300 parts, 12 were defective. On the basis of these data, can the machine be qualified?
The article “Developing a Tool to Measure the Factors Influencing Nurses’ Enjoyment of Nursing”(L. Wilkes, M. Doull, et al., Journal of Clinical Nursing, 2016:1854–1860) reports that in a sample of 124 nurses, 54 said that a busy workload had a positive effect on their enjoyment of their
The anterior cruciate ligament (ACL) runs diagonally in the middle of the knee. The article ‘‘Return to Sport After Pediatric Anterior Cruciate Ligament Reconstruction and Its Effect on Subsequent Anterior Cruciate Ligament Injury’’ (T. Dekker, J. Godin, et al., Journal of Bone and Joint
In a survey of 500 residents in a certain town, 274 said they were opposed to constructing a new shopping mall. Can you conclude that more than half of the residents in this town are opposed to constructing a new shopping mall?
The article “Evaluation of Criteria for Setting Speed Limits on Gravel Roads” (S. Dissanayake, Journal of Transportation Engineering, 2011:57–63) measured speeds of vehicles on several roads in the state of Kansas. On South Cedar Niles, 73 vehicles were observed, and 49 of them were exceeding
Do bathroom scales tend to underestimate a person’s true weight? A 150 lb test weight was placed on each of 50 bathroom scales. The readings on 29 of the scales were too light, and the readings on the other 21 were too heavy. Can you conclude that more than half of bathroom scales underestimate
The article “HIV-positive Smokers Considering Quitting: Differences by Race/Ethnicity” (E. LloydRichardson, C. Stanton, et al., Am J Health Behav, 2008:3–15) surveyed 444 HIV-positive smokers. Of these, 281 were male and 163 were female. Consider this to be a simple random sample. Can you
Gravel pieces are classified as small, medium, or large. A vendor claims that at least 10% of the gravel pieces from her plant are large. In a random sample of 1600 pieces, 130 pieces were classified as large. Is this enough evidence to reject the claim?
The following MINITAB output presents the results of a hypothesis test for a population mean ????.One-Sample Z: X Test of mu = 37 vs not = 37 The assumed standard deviation = 3.2614 Variable N Mean StDev SE Mean 95% CI Z P X 87 36.5280 3.2614 0.3497 (35.8247, 37.2133) −1.35 0.177a. Can H0 be
A new method of teaching arithmetic to elementary school students was evaluated. The students who were taught by the new method were given a standardized test with a maximum score of 100 points. They scored an average of one point higher than students taught by the old method. A hypothesis test was
A new method of postoperative treatment was evaluated for patients undergoing a certain surgical procedure. Under the old method, the mean length of hospital stay was 6.3 days. The sample mean for the new method was 6.1 days. A hypothesis test was performed in which the null hypothesis stated that
Refer to Exercise 18. It is discovered that the standard deviation of the sample used to compute the confidence interval is 5 N. Is it possible to determine whether P < 0.01? Explain.
Refer to Exercise 17. It is discovered that the mean of the sample used to compute the confidence bound is X = 3.40. Is it possible to determine whether P < 0.01? Explain.
A shipment of fibers is not acceptable if the mean breaking strength of the fibers is less than 50 N. A large sample of fibers from this shipment was tested, and a 98% lower confidence bound for the mean breaking strength was computed to be 50.1 N. Someone suggests using these data to test the
The strength of a certain type of rubber is tested by subjecting pieces of the rubber to an abrasion test. For the rubber to be acceptable, the mean weight loss ????must be less than 3.5 mg. A large number of pieces of rubber that were cured in a certain way were subject to the abrasion test. A 95%
A scientist computes a 90% confidence interval to be(4.38, 6.02). Using the same data, she also computes a 95% confidence interval to be (4.22, 6.18), and a 99% confidence interval to be (3.91, 6.49). Now she wants to test H0 : ???? = 4 versus H1 : ???? ≠ 4. Regarding the P-value, which one of
Refer to Exercise 14. For which null hypothesis will P = 0.05?i. H0 : ???? = 1.2 ii. H0 : ???? ≤ 1.2 iii. H0 : ???? ≥ 1.2
Fill in the blank: A 95% confidence interval for ???? is(1.2, 2.0). Based on the data from which the confidence interval was constructed, someone wants to test H0 : ???? = 1.4 versus H1 : ???? ≠ 1.4. The P-value will be .i. greater than 0.05 ii. less than 0.05 iii. equal to 0.05
A method of applying zinc plating to steel is supposed to produce a coating whose mean thickness is no greater than 7 microns. A quality inspector measures the thickness of 36 coated specimens and tests H0 : ???? ≤ 7 versus H1 : ???? > 7. She obtains a P-value of 0.40. Since P > 0.05, she
A machine that fills cereal boxes is supposed to be calibrated so that the mean fill weight is 12 oz. Let ????denote the true mean fill weight. Assume that in a test of the hypotheses H0 : ???? = 12 versus H1 : ???? ≠ 12, the P-value is 0.30.a. Should H0 be rejected on the basis of this test?
A test is made of the hypotheses H0 : ???? = 10 versus H1 : ???? ≠ 10.Consider three possible conclusions: (i) The scale is in calibration. (ii) The scale is out of calibration.(iii) The scale might be in calibration.a. Which of the three conclusions is best if H0 is rejected?b. Which of the
It is desired to check the calibration of a scale by weighing a standard 10 g weight 100 times. Let ????be the population mean reading on the scale, so that the scale is in calibration if ???? =
The installation of a radon abatement device is recommended in any home where the mean radon concentration is 4.0 picocuries per liter (pCi/L) or more, because it is thought that long-term exposure to sufficiently high doses of radon can increase the risk of cancer. Seventy-five measurements are
In each of the following situations, state the most appropriate null hypothesis regarding the population mean ????.a. A new type of battery will be installed in heart pacemakers if it can be shown to have a mean lifetime greater than 8 years.b. A new material for manufacturing tires will be used if
Let ???? be the radiation level to which a radiation worker is exposed during the course of a year. The Environmental Protection Agency has set the maximum safe level of exposure at 5 rem per year. If a hypothesis test is to be performed to determine whether a workplace is safe, which is the most
Scores on a certain IQ test are known to have a mean of 100. A random sample of 60 students attend a series of coaching classes before taking the test. Let ???? be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if ???? > 100. A
George performed a hypothesis test. Luis checked George’s work by redoing the calculations. Both George and Luis agree that the result was statistically significant the 5% level, but they got different P-values. George got a P-value of 0.20, and Luis got a P-value of 0.02.a. Is it possible that
True or false: If P = 0.02, thena. The result is statistically significant at the 5% level.b. The result is statistically significant at the 1% level.c. The null hypothesis is rejected at the 5% level.d. The null hypothesis is rejected at the 1% level.
If P = 0.50, which is the best conclusion?i. H0 is definitely false.ii. H0 is definitely true.iii. There is a 50% probability that H0 is true.iv. H0 is plausible, and H1 is false.v. Both H0 and H1 are plausible.
If P = 0.01, which is the best conclusion?i. H0 is definitely false.ii. H0 is definitely true.iii. There is a 1% probability that H0 is true.iv. H0 might be true, but it’s unlikely.v. H0 might be false, but it’s unlikely.vi. H0 is plausible.
For which P-value is the null hypothesis more plausible: P = 0.10 or P = 0.01?
The following MINITAB output presents the results of a hypothesis test for a population mean ????. Some of the numbers are missing. Fill them in.One-Sample Z: X Test of mu = 3.5 vs > 3.5 The assumed standard deviation = 2.00819 95%Lower Variable N Mean StDev SE Mean Bound Z P X 87 4.07114 2.00819
The following MINITAB output presents the results of a hypothesis test for a population mean ????. Some of the numbers are missing. Fill them in.One-Sample Z: X Test of mu = 10.5 vs < 10.5 The assumed standard deviation = 2.2136 95%Upper Variable N Mean StDev SE Mean Bound Z P X (a) (b) 2.2136
The following MINITAB output presents the results of a hypothesis test for a population mean ????.
Fill volumes, in oz, of a large number of beverage cans were measured, with X = 11.98 and ????X = 0.02.Use this information to find the P-value for testing H0 : ???? = 12.0 versus H1 : ???? ≠ 12.0.
An automotive engineer subjects a large number of brake pads to a stress test and measures the wear on each. She obtains X = 7.4 mm and ????X = 0.2 mm.Use this information to find the P-value for testing H0 : ???? = 7.0 versus H1 : ???? ≠ 7.0.
Fill in the blank: In a test of H0 : ???? = 5 versus H1 :???? ≠ 5, the sample mean was X = 4, and the P-value was 0.22. This means that if ???? = 5, and the experiment were repeated 100 times, we would expect to obtain a value of X between 4 and 6 approximately times.i. 4 ii. 22 iii. 78 iv. 6
Fill in the blank: In a test of H0 : ???? ≥10 versus H1 : ????
Fill in the blank: If the null hypothesis is H0 : ???? ≤4, then the mean of X under the null distribution is.i. 0 ii. 4 iii. Any number less than or equal to 4.iv. We can’t tell unless we know H1.
A new concrete mix is being designed to provide adequate compressive strength for concrete blocks.The specification for a particular application calls for the blocks to have a mean compressive strength???? greater than 1350 kPa. A sample of 100 blocks is produced and tested. Their mean compressive
The article “Predicting Profit Performance for Selecting Candidate International Construction Projects”(S. Han, D. Kim, and H. Kim, Journal of Construction Engineering and Management Science, 2007:425–436) presents an analysis of the profit of international construction projects. In a sample
Lasers can provide highly accurate measurements of small movements. To determine the accuracy of such a laser, it was used to take 100 measurements of a known quantity. The sample mean error was 25 ????m with a standard deviation of 60 ????m. The laser is properly calibrated if the mean error is
When it is operating properly, a chemical plant has a mean daily production of at least 740 tons. The output is measured on a simple random sample of 60 days. The sample had a mean of 715 tons/day and a standard deviation of 24 tons/day. Let ???? represent the mean daily output of the plant. An
A certain type of stainless steel powder is supposed to have a mean particle diameter of ???? = 15 ????m. A random sample of 87 particles had a mean diameter of 15.2 ????m, with a standard deviation of 1.8 ????m. A test is made of H0 : ???? = 15 versus H1 : ???? ≠ 15.a. Find the P-value.b. Do you
A sample of 50 copper wires had a mean resistance of 1.03 mΩ with a standard deviation of 0.1 mΩ. Let ????represent the mean resistance of copper wires of this type.a. Find the P-value for testing H0 : ???? ≤ 1 versus H1 : ???? > 1.b. Either the mean resistance is greater than 1 mΩ, or the
In a process that manufactures tungsten-coated silicon wafers, the target resistance for a wafer is 85 mΩ.In a simple random sample of 50 wafers, the sample mean resistance was 84.8 mΩ, and the standard deviation was 0.5 mΩ. Let ???? represent the mean resistance of the wafers manufactured by
The article “Supply Voltage Quality in Low-Voltage Industrial Networks of Estonia” (T. Vinnal, K. Janson, et al., Estonian Journal of Engineering, 2012:102–126) presents voltage measurements for a sample of 66 industrial networks in Estonia. Assume the rated voltage for these networks is 232
The pH of an acid solution used to etch aluminum varies somewhat from batch to batch. In a sample of 50 batches, the mean pH was 2.6, with a standard deviation of 0.3. Let ???? represent the mean pH for batches of this solution.a. Find the P-value for testing H0 : ???? ≤ 2.5 versus H1 : ???? >
Recently, many companies have been experimenting with telecommuting, allowing employees to work at home on their computers. Among other things, telecommuting is supposed to reduce the number of sick days taken. Suppose that at one firm, it is known that over the past few years employees have taken
The answer to Exercise 23 part (d) is needed for this exercise. A geologist counts 64 emitted particles in one minute from a certain radioactive rock.a. Find a 95% confidence interval for the rate of emissions in units of particles per minute.b. After four minutes, 256 particles are counted. Find a
Let X represent the number of events that are observed to occur in n units of time or space, and assume X ∼ Poisson(n????), where ???? is the mean number of events that occur in one unit of time or space. Assume X is large, so that X ∼ N(n????, n????). Follow steps(a) through (d) to derive a
Boxes of nails contain 100 nails each. A sample of 10 boxes is drawn, and each of the boxes is weighed. The average weight is 1500 g, and the standard deviation is 5 g. Assume the weight of the box itself is negligible, so that all the weight is due to the nails in the box.a. Let ????box denote the
The temperature of a certain solution is estimated by taking a large number of independent measurements and averaging them. The estimate is 37◦C, and the standard error is 0.1◦C.a. Find a 95% confidence interval for the temperature.b. What is the confidence level of the interval 37 ±0.1◦C?c.
A meteorologist measures the temperature in downtown Denver at noon on each day for one year. The 365 readings average 57◦F and have standard deviation 20◦F. The meteorologist computes a 95% confidence interval for the mean temperature at noon to be 57◦ ± (1.96)(20)∕√ 365. Is this
A large box contains 10,000 ball bearings. A random sample of 120 is chosen. The sample mean diameter is 10 mm, and the standard deviation is 0.24 mm. True or false:a. A 95% confidence interval for the mean diameter of the 120 bearings in the sample is 10 ±(1.96)(0.24)∕√120.b. A 95% confidence
Sixty-four independent measurements were made of the speed of light. They averaged 299,795 km/s and had a standard deviation of 8 km/s. True or false:a. A 95% confidence interval for the speed of light is 299,795 ± 1.96 km/s.b. The probability is 95% that the speed of light is in the interval
Based on a large sample of capacitors of a certain type, a 95% confidence interval for the mean capacitance, in ????F, was computed to be (0.213, 0.241). Find a 90% confidence interval for the mean capacitance of this type of capacitor.
A 95% confidence interval for a population mean is computed from a sample of size 400. Another 95%confidence interval will be computed from a sample of size 100 drawn from the same population.Choose the best answer to fill in the blank: The interval from the sample of size 400 will be approximately
An investigator computes a 95% confidence interval for a population mean on the basis of a sample of size 70. If she wishes to compute a 95% confidence interval that is half as wide, how large a sample does she need?
The carbon content (in ppm) was measured for each of six silicon wafers. The results were 2.41 2.45 2.21 2.32 2.25 2.38 Assume that carbon contents are normally distributed.a. Find a 95% prediction interval for the carbon content of a single wafer.b. Find a tolerance interval for the carbon content
Diameters, in mm, were measured for eight specimens of a certain type of ball bearing. The results were 8.4 8.2 9.5 9.3 8.8 9.8 8.5 9.1 Assume the diameters are normally distributed.a. Find a 98% prediction interval for the diameter of a single ball bearing.b. Find a tolerance interval for the
In a study of the lifetimes of electronic components, a random sample of 400 components are tested until they fail to function. The sample mean lifetime was 370 hours and the standard deviation was 650 hours.True or false:a. An approximate 95% confidence interval for the mean lifetime of this type
A metallurgist makes several measurements of the melting temperature of a certain alloy and computes a 95% confidence interval to be 2038 ± 2◦C. Assume the measuring process for temperature is unbiased.True or false:a. There is 95% probability that the true melting temperature is in the interval
Refer to Exercise 9. A device will be manufactured in which two of the components in Exercise 9 will be connected in series. The components function independently, and the device will function only if both components function. Let q be the probability that a device functions. Find a 95% confidence
A random sample of 400 electronic components manufactured by a certain process are tested, and 30 are found to be defective.a. Let p represent the proportion of components manufactured by this process that are defective.Find a 95% confidence interval for p.b. How many components must be sampled so
A sample of 100 components is drawn, and a 95%confidence interval for the proportion defective specifies this proportion to within ±0.06. To get a more precise estimate of the number defective, the sample size will be increased to 400, and the confidence interval will be recomputed. What will be
A 99% confidence interval for a population mean based on a sample of size 64 is computed to be(16.3, 18.7). How large a sample is needed so that a 99% confidence interval will specify the mean to within ±1.0?
In a random sample of 53 concrete specimens, the average porosity (in %) was 21.6, and the standard deviation was 3.2.a. Find a 90% confidence interval for the mean porosity of specimens of this type of concrete.b. Find a 95% confidence interval for the mean porosity of specimens of this type of
A survey is to be conducted in which a random sample of residents in a certain city will be asked whether they favor or oppose a modernization project for the civic center. How many residents should be polled to be sure that a 98% confidence interval for the proportion who are in favor specifies
A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5%, and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed. Find a 99%
Three confidence intervals for the mean shear strength(in ksi) of anchor bolts of a certain type are computed, all from the same sample. The intervals are(4.01, 6.02), (4.20, 5.83), and (3.57, 6.46). The levels of the intervals are 90%, 95%, and 99%. Which interval has which level?
In a sample of 150 boards of a certain grade, the average modulus of elasticity was 1.57 psi, and the standard deviation was 0.23 psi.a. Find a 95% confidence interval for the mean modulus of elasticity.b. Find a 99.5% confidence interval for the mean modulus of elasticity.c. What is the confidence
Concentrations of atmospheric pollutants such as carbon monoxide (CO) can be measured with a spectrophotometer. In a calibration test, 50 measurements were taken of a laboratory gas sample that is known to have a CO concentration of 70 parts per million(ppm). A measurement is considered to be

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