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statistics for engineers and scientists
Statistics For Engineers And Scientists 6th Edition William Navidi - Solutions
Using the results of Exercises 38 and 39, can you conclude that the mean FEV1 differs between those who have asthma and those who don't?Data From Exercise 39:Refer to Exercise 38. Repeat this test, using only those 10.82 years old or younger.Data From Exercise 38:The median age for people in the
The article "Bioremediation of Soil Contaminated Crude Oil by Agaricomycetes" (Mohammad-Sichani, Assadi, et al., Journal of Environmental Health and Engineering, 2017, online) describes an experiment to determine the effectiveness of mushroom compost in removing petroleum contaminants from soil.
The article "Weekly Personal Ozone Exposure and Respiratory Health in a Panel of Greek Schoolchildren" (A. Karakatsani, E. Samoli, et al., Environmental Health Perspectives, 2017, online) describes a study of the health effects of ozone air pollution on children's health. Out of 70 children who
In a sample of 100 automobiles driven at high altitude, \(17 \%\) exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. The same cars were driven at sea level, and \(11 \%\) of them exceeded the standard. Let \(p_{1}\) be the proportion of automobiles that exceed the
Refer to the data set lung.csv. The median ozone for all individuals in the study is 32.48. Can you conclude that people whose ozone exposure is greater than the median are more likely to have asthma than those whose exposure is less than or equal to the median?Lung Data Set:Forced expiratory
Refer to the data set weather.csv. Can you conclude that the proportion of times the record maximum has occurred after 1945 is greater than the proportion of times the record minimum has occurred after 1945?Weather Data Set:This data set contains the record high and low temperatures in Washington,
The article "Prediction of Performance and Evaluation of Flexible Pavement Rehabilitation Strategies" (K. Lee, K. Wilson, and S. Hassan, Journal of Traffic and Transportation Engineering, 2017:178-184) describes methods used to rehabilitate Route 165 in the town of Exeter, Rhode Island. The
In an experiment to determine whether there is a systematic difference between the weights obtained with two different scales, 10 rock specimens were weighed, in grams, on each scale. The following data were obtained:Can you conclude that the mean weight on scale 2 is greater than the mean weight
The following output (from \(\mathrm{R}\) ) presents the results of a hypothesis test for the difference \(\mu_{X}-\mu_{Y}\) between two population means:a. Is this a one-tailed or a two-tailed test?b. What is the null hypothesis?c. Can \(H_{0}\) be rejected at the \(5 \%\) level? How can you
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 males and females with diabetes. Each respondent was categorized by gender and income level. The numbers in
Refer to the data set pit.csv. A pit is classified as "deep" if its depth is greater than \(30 \mu \mathrm{m}\). Consider pits at \(40 \%\) humidity. Can you conclude that the proportion of pits that are deep varies with duration?Pit Data Set:In an experiment to measure corrosion in stainless
Refer to the data set tunnel.csv. Can you conclude that the proportion of times that the speed is greater than 50 mm/min50 mm/min varies with the type of soil?Tunnel Data Set:A tunnel boring machine, used to construct underground tunnels, contains a large circular cutting wheel which rotates as
A company that manufactures steel wires guarantees that the mean breaking strength (in \(\mathrm{kN}\) ) of the wires is greater than 50 . They measure the strengths for a sample of wires and test \(H_{0}: \mu \leq 50\) versus \(H_{1}: \mu>50\).a. If a type I error is made, what conclusion will be
Washers used in a certain application are supposed to have a thickness of 2 millimeters. A quality control engineer measures the thicknesses for a sample of washers and tests \(H_{0}: \mu=2\) versus \(H_{1}: \mu eq 2\).a. If a type I error is made, what conclusion will be drawn regarding the mean
Let \(\mu\) denote the mean yield strength of a certain type of steel bar, in units of \(\mathrm{mPa}\). A test will be made of \(H_{0}: \mu \leq 250\) versus \(H_{1}: \mu>250\). Three rejection regions are considered: (i) \(\bar{X}>258.4\), (ii) \(\bar{X}>261.9\), and (iii) \(\bar{X}>256.5\). The
It is desired to check the calibration of a scale by weighing a standard 10 -gram weight 100 times. Let \(\mu\) be the population mean reading on the scale, so that the scale is in calibration if \(\mu=10\) and out of calibration if \(\mu eq 10\). A test is made of the hypotheses \(H_{0}: \mu=10\)
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 \(\mu\) be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if
The rejection region for a \(5 \%\) level test of \(H_{0}: \mu \geq 10\) versus \(H_{1}: \mu
A coin has probability \(p\) of landing heads when tossed. A test will be made of the hypotheses \(H_{0}: p \leq 0.1\) ver- sus \(H_{1}: p>0.1\), as follows. The coin will be tossed once. If it comes up heads, \(H_{0}\) will be rejected. If it comes up tails, \(H_{0}\) will not be rejected.a. If
The following output (from \(\mathrm{R}\) ) presents the results of a power calculation for a test of the difference between two means \(\mu_{1}-\mu_{2}\).a. Is the power calculated for a one-tailed or a two-tailed test?b. If the sample sizes were 50 in each group, would the power be less than 0.9
Refer to the data set pit.csv.a. Consider pits at 4 weeks duration. Perform a randomization test to determine whether the mean depth at \(40 \%\) relative humidity differs from that at \(70 \%\) relative humidity.b. Repeat for pits at 26 weeks duration.c. Repeat for pits at 52 weeks duration.Pit
Refer to the data set gravity.csv. Generate 1000 bootstrap samples. Let \(\mu\) represent the population mean measurement of the acceleration due to gravity. Using the bootstrap data you generated, can you reject the null hypothesis \(H_{0}: \mu
A team of automotive engineers want to compare the lifetimes of two brands of tire. They obtain samples of seven tires of each brand. On each of seven cars, they mount one tire of each brand on each front wheel. The cars are driven until only \(20 \%\) of the original tread remains. The distances,
A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in millimeters of mercury
Foot ulcers are a common problem for people with diabetes. Higher skin temperatures on the foot indicate an increased risk of ulcers. The article "An Intelligent Insole for Diabetic Patients with the Loss of Protective Sensation" (Kimberly Anderson, M.S. Thesis, Colorado School of Mines) reports
A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in \(\mathrm{mmHg}\), for
Concrete expands both horizontally and vertically over time. The article "Evaluation of the Expansion Attained to Date by Concrete Affected by AlkaliSilica Reaction. Part III: Application to Existing Structures" (M. Bérubé, N. Smaoui, et al., Canadian Journal of Civil Engineering, 2005:463-479)
Carrie and Javier have both computed the slope of the least-squares line using data for which the standard deviation of the \(x\) values and the standard deviation of the \(y\) values are equal. Carrie gets a value of 0.5 for the slope, and Javier gets a value of 2. One of them is right. Which one?
Refer to the data set lung.csv.a. Compute the least-squares line for predicting FEV1 from ozone exposure.b. Let \(\beta_{1}\) denote the change in FEV1 associated with an increase of \(1 \mathrm{ppb}\) in ozone level. Test the hypothesis \(H_{0}: \beta_{1} \geq 0\) versus \(H_{1}: \beta_{1}c.
Refer to Exercise 18. Which of the following is the best conclusion to be drawn from the results?i. Higher exposure to ozone is associated with lower values of FEV1, but the value of the correlation shows that the association is weak.ii. Higher exposure to ozone is associated with lower values of
How much noisier are streets where cars travel faster? The article "Modeling of Urban Area Stop-and-Go Traffic Noise" (P. Pamanikabud and C. Tharasawatpipat, Journal of Transportation Engineering, 1999:152-159) reports noise levels in decibels and average speed in kilometers per hour for a sample
In the following \(\mathrm{R}\) output, some of the numbers have been accidentally erased. Recompute them, using the numbers still available. There are \(n=25\) points in the data set. Coefficients: (Intercept) X Estimate 1.71348 4.27473 Std. Error 6.69327 (c) t value (a) 3.768 Pr(>|t|) (b) (d)
In the following \(R\) output, some of the numbers have been accidentally erased. Recompute them, using the numbers still available. There are \(n=20\) points in the data set. Coefficients: (Intercept) X Estimate (a) 0.18917 Std. Error 0.43309 0.06573 t value 0.688 (c) Pr (>|t|) (b) (d)
The distance advanced in a day by a tunnel boring machine, in meters, is uniformly distributed on the inter\(\operatorname{val}(30,50)\).a. Find the mean distance.b. Find the standard deviation of the distances.c. Find the probability that the distance is between 35 and 42 meters.d. Suppose the
Let \(T \sim \Gamma(4,0.5)\).a. Find \(\mu_{T}\).b. Find \(\sigma_{T}\).c. Find \(P(T \leq 1)\).d. Find \(P(T \geq 4)\).
Let \(T \sim \Gamma(r, \lambda)\). If \(\mu_{T}=8\) and \(\sigma_{T}^{2}=16\), find \(r\) and \(\lambda\).
Let \(T \sim \Gamma(r, \lambda)\). If \(\mu_{T}=8\) and \(r=16\), find \(\lambda\) and \(\sigma^{2}\).
Let \(T \sim \operatorname{Weibull}(0.5,3)\).a. Find \(\mu_{T}\).b. Find \(\sigma_{T}\).c. Find \(P(T5)\).e. Find \(P(2
Let \(X_{1}, \ldots, X_{n}\) be a random sample from a population with the Poisson \((\lambda)\) distribution. Find the MLE of \(\lambda\).
Let \(X_{1}, \ldots, X_{n}\) be a random sample from a \(N(\mu, 1)\) population. Find the MLE of \(\mu\).
Consider the following data set:a. Construct a normal probability plot for these data. Do the data appear to come from an approximately normal distribution?b. Transform the data by taking the square root of each value in the data set. Show that the square roots appear to come from an approximately
Consider the following data set:a. Construct a normal probability plot for these data. Do the data appear to come from an approximately normal distribution?b. Transform the data by taking the reciprocal of each value in the data set. Show that the reciprocals appear to come from an approximately
Among all monthly bills from a certain credit card company, the mean amount billed was \(\$ 485\) and the standard deviation was \(\$ 300\). In addition, for \(15 \%\) of the bills, the amount billed was greater than \(\$ 1000\). A sample of 900 bills is drawn.a. What is the probability that the
The time taken by an automobile mechanic to complete an oil change is random, with mean 29.5 minutes and standard deviation 3 minutes.a. What is the probability that 50 oil changes take more than 1500 minutes?b. What is the probability that a mechanic can complete 80 or more oil changes in 40
Concrete blocks are produced in lots of 2000 . Each block has probability 0.85 of meeting a strength specification. The blocks are independent.a. What is the probability that, in a given lot, fewer than 1690 blocks meet the specification?b. Find the 70th percentile of the number of blocks that meet
Refer to Exercise 13. Assume the distribution from which the sample was drawn is unknown. We want to estimate the population mean μμμμ with the sample mean ¯X¯XX¯¯X. This exercise shows how to use the nonparametric bootstrap to estimate the bias and uncertainty in
Medication used to treat a certain condition is administered by syringe. The target dose in a particular application is \(\mu\). Because of the variations in the syringe, in reading the scale, and in mixing the fluid suspension, the actual dose administered is normally distributed with mean \(\mu\)
Three confidence intervals for a population mean are constructed, all from the same random sample. The confidence levels are 95\%, 98\%, and 99.9\%. The confidence intervals are \((6.4,12.3),(5.1,13.6)\), and \((6.8\), 11.9). Match each confidence interval to its level.
A sample of 114 patients were given a drug to lower cholesterol. A 95\% confidence interval for the mean reduction in cholesterol (in \(\mathrm{mmol} / \mathrm{L}\) ) was \((0.88,1.02)\).a. What was the sample mean reduction?b. What was the sample standard deviation of the reduction amounts?
In a sample of 80 light bulbs, the mean lifetime was 1217 hours. Assume the population standard deviation is 52 hours.a. Find a 95\% confidence interval for the mean lifetime of this type of light bulb.b. Find a \(98 \%\) confidence interval for the mean lifetime of this type of light bulb.c. An
Refer to Exercise 7.a. Find a \(90 \%\) upper confidence bound for the mean lifetime.b. Someone says that the mean lifetime is less than 1220 hours. With what level of confidence can this statement be made?Data From Exercise 7:In a sample of 80 light bulbs, the mean lifetime was 1217 hours. Assume
Refer to Exercise 8.a. Find a 98\% lower confidence bound for the mean efficiency.b. The claim is made that the mean efficiency is greater than \(84.6 \%\). With what level of confidence can this statement be made?Data From Exercise 8:In a sample of 60 electric motors, the average efficiency (in
A chemist made six independent measurements of the sublimation point of carbon dioxide (the temperature at which it changes to dry ice). The sample mean was \(196.64 \mathrm{~K}\) with a standard deviation of \(0.68 \mathrm{~K}\).a. Use the Student's \(t\) distribution to find a \(95 \%\)
In a sample of 100 steel canisters, the mean wall thickness was \(8.1 \mathrm{~mm}\) with a standard deviation of \(0.5 \mathrm{~mm}\).a. Find a 95\% confidence interval for the mean wall thickness of this type of canister.b. Find a \(99 \%\) confidence interval for the mean wall thickness of this
A sample of 75 concrete blocks had a mean mass of \(38.3 \mathrm{~kg}\) with a standard deviation of \(0.6 \mathrm{~kg}\).a. Find a 95\% confidence interval for the mean mass of this type of concrete block.b. Find a \(99 \%\) confidence interval for the mean mass of this type of concrete block.c.
One step in the manufacture of a certain metal clamp involves the drilling of four holes. In a sample of 150 clamps, the average time needed to complete this step was 72 seconds and the standard deviation was 10 seconds.a. Find a 95\% confidence interval for the mean time needed to complete this
Refer to Exercise 14.a. Find a \(95 \%\) upper confidence bound for the mean improvement.b. Find a \(98 \%\) lower confidence bound for the mean improvement.Data From Exercise 14:The article "Modeling Arterial Signal Optimization with Enhanced Cell Transmission Formulations" (Z. Li, Journal of
Refer to Exercise 15.a. Find a \(95 \%\) lower confidence bound for the mean wall thickness.b. Find a \(99 \%\) upper confidence bound for the mean wall thickness.Data From Exercise 15:In a sample of 100 steel canisters, the mean wall thickness was \(8.1 \mathrm{~mm}\) with a standard deviation of
Refer to Exercise 16.a. Find a \(95 \%\) lower confidence bound for the mean time.b. Find a \(90 \%\) upper confidence bound for the mean time.Data From Exercise 16:The article "Application of Surgical Navigation to Total Hip Arthroplasty" (T. Ecker and S. Murphy, Journal of Engineering in
Refer to Exercise 17.a. Find a 95%95% upper confidence bound for the mean mass.b. Find a 99.5%99.5% lower confidence bound for the mean mass.Data From Exercise 17:A sample of 75 concrete blocks had a mean mass of \(38.3 \mathrm{~kg}\) with a standard deviation of \(0.6 \mathrm{~kg}\).
Refer to Exercise 18.a. Find a 95%95% upper confidence bound for the mean time.b. Find a 98%98% lower confidence bound for the mean time.Data From Exercise 18:One step in the manufacture of a certain metal clamp involves the drilling of four holes. In a sample of 150 clamps, the average time needed
Refer to Exercise 19.a. Find a 95%95% lower confidence bound for the mean weight.b. Find a 90%90% upper confidence bound for the mean weight.Data From Exercise 19:In a sample of 80 ten-penny nails, the average weight was \(1.56 \mathrm{~g}\) and the standard deviation was \(0.1 \mathrm{~g}\).
An investigator computes a \(95 \%\) confidence interval for a population mean on the basis of a sample of size 70. Approximately how large a sample is needed to produce a 95\% confidence interval that is half as wide?
The concentration of carbon monoxide (CO) in a gas sample is measured by a spectrophotometer and found to be \(85 \mathrm{ppm}\). Through long experience with this instrument, it is believed that its measurements are unbiased and normally distributed, with population standard deviation \(8
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.a. In a sample of 8
Refer to the data set pit.csv. Find a confidence interval of the specified level for the mean depth of pits for the following durations and humidity levels. When the sample size is 30 or less, construct a dotplot to determine whether it is appropriate to construct a confidence interval.a. Four
Refer to Exercise 32. For each duration, the confidence interval at 40%40% humidity is narrower than the one at 75%75% humidity. Which of the following is the best explanation for this?i. There are more pits at 40%40% humidity than at 75%75%, and there is greater spread in their depths.ii. There
Refer to the data set tunnel.csv. Find a confidence interval of the specified level for the mean speed in each of the following types of soil.a. GSG soil, 95%95% confidenceb. CCS soil, 98%98% confidencec. GSF soil, 99%99% confidenced. GSGu soil, 90%90% confidenceTunnel Data Set:A tunnel boring
Find a confidence interval of the specified level for the mean torque in each of the following types of soil.a. GSG soil, \(95 \%\) confidenceb. CCS soil, \(98 \%\) confidencec. GSF soil, \(99 \%\) confidenced. GSGu soil, \(90 \%\) confidence
Refer to the data set gravity.csv.a. How many outliers are in the data?b. Explain why it is appropriate to use the methods of this section to find a confidence interval for the mean, even though the data contain outliers.c. Find a 95\% confidence interval for the mean measurement of the
The National Center for Health Statistics interviewed 5409 adult smokers in 2015 , and 2636 of them said they had tried to quit smoking during the past year. Consider this to be a random sample.a. Find a 95\% confidence interval for the proportion of smokers who have tried to quit within the past
High levels of blood sugar are associated with an increased risk of type 2 diabetes. A level higher than normal is referred to as "impaired fasting glucose." The article "Association of Low-Moderate Arsenic Exposure and Arsenic Metabolism with Incident Diabetes and Insulin Resistance in the Strong
Refer to Exercise 4. Find a \(99 \%\) lower confidence bound for the proportion of smokers who tried to quit smoking in the past year.Data From Exercise 4:The National Center for Health Statistics interviewed 5409 adult smokers in 2015, and 2636 of them said they had tried to quit smoking during
Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequently to breathe. The article "Postoperative Complications in Patients With Obstructive Sleep Apnea Syndrome Undergoing Hip or Knee Replacement: A Case-Control Study" (R.
Refer to the data set pit.csv. Pits with depths greater than \(30 \mu \mathrm{m}\) are considered "deep." Find a confidence interval of the specified level for the proportion of pits that are deep for each of the following durations and humidity levels.a. Four weeks at \(40 \%\) relative humidity,
Which of the following statements best summarizes the results of Exercise 17?i. The number of pits is less at \(75 \%\) humidity than at \(40 \%\), but the proportion that are deep is about the same or greater.ii. The number of pits is less at \(75 \%\) humidity than at \(40 \%\), and the
Refer to the data set gravity.csv. The measurements are expressed in deviations from a base value of about \(9.8 \mathrm{~m} / \mathrm{s}^{2}\), in units of \(10^{-8} \mathrm{~m} / \mathrm{s}^{2}\). Find a \(95 \%\) confidence interval for the proportion of measurements that are greater than the
The article "Utility of Pretest Probability and Exercise Treadmill Test in Korean Women with Suspected Coronary Artery Disease" (Y. Kim, W. Shim, et al., Journal of Women's Health, 2015:617-622) presents a study of health outcomes in women with symptoms of heart disease. In a sample of 110 women
The article "Effects of Diets with Whole PlantOrigin Proteins Added with Different Ratios of Taurine:Methionine on the Growth, Macrophage Activity and Antioxidant Capacity of Rainbow Trout (Oncorhynchus mykiss) Fingerlings" (O. Hernandez, L. Hernandez, et al., Veterinary and Animal Science,
In a sample of 90 large grade A eggs, the mean number of calories was 70 with a standard deviation of 2.5. In a sample of 85 large grade AA eggs, the mean number of calories was 80 with a standard deviation of 2.7. Find a \(98 \%\) confidence interval for the mean difference in the number of
The article "Treadmill Exercise and Resistance Training in Patients With Peripheral Arterial Disease With and Without Intermittent Claudication. A Randomized Controlled Trial" (M. McDermott, P. Ades, et al., Journal of the American Medical Association, 2009:165-174) reported the results of a study
In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Sixteen randomly selected plots of land were treated with fertilizer A. The average yield, in pounds, was 457 with a standard deviation of 38 . Twelve randomly selected plots were treated with
In a test to compare yield strengths of two grades of carbon steel bolts, strengths of eight grade 2 bolts and six grade 5 bolts were measured. The results, in MPa, wereFind a \(98 \%\) confidence interval for the difference between the mean yield strengths for grade 5 and grade 2 bolts. Grade 2:
For each of the following types of soil, find the median torque and median speed for all observations in that soil.a. GSG soilb. CCS soilc. GSF soild. GSGu soil
Which statement best describes the results of Exercise 30 ?i. For soils where the median torque is greater, the median speed is greater.ii. For soils where the median torque is greater, the median speed is less.Data From Exercise 30:For each of the following types of soil, find the median torque
For each of the following types of soil, find the median value of the torque for all observations in that soil. Then let \(\mu_{L}\) be the mean speed when the torque is below the median, let \(\mu_{U}\) be the mean speed when the torque is above the median, and find a \(95 \%\) confidence interval
Which statement best describes the results of Exercise 32 ?i. For each of the four soils, we are \(95 \%\) confident that the mean speed is greater when the torque is lower.ii. For each of the four soils, we are \(95 \%\) confident that the mean speed is greater when the torque is greater.Data From
Refer to Exercises 31 and 33. The relationship between median torques and median speeds is called the relationship between soils. The relationships between torque and speed restricted to a certain soil are called the relationships within soils. Is the relationship within soils the same as the
Compute the median torque for all observations in all soils. Let \(\mu_{L}\) be the mean speed when the torque is below the median, and let \(\mu_{U}\) be the mean speed when the torque is above the median. Find a \(95 \%\) confidence interval for \(\mu_{U}-\mu_{L}\).
Which statement best describes the results of Exercise 35 ?i. For observations over all soils, we are 95\% confident that the mean speed is greater when the torque is lower.ii. For observations over all soils, we are 95\% confident that the mean speed is greater when the torque is greater.Data From
Is the relationship between torque and speed computed from all soils combined more like the withinsoils relationship or the between-soils relationship?
For each of the following durations, find a confidence interval of the specified level for the difference between the mean depth at \(40 \%\) relative humidity and the mean depth at \(75 \%\) relative humidity.a. Four weeks, \(95 \%\) confidenceb. 26 weeks, \(90 \%\) confidencec. 52 weeks, \(99
Find a confidence interval of the specified level for the difference in mean pit depth for each of the following values for humidity and pairs of durations.a. \(40 \%\) humidity: Difference between mean pit depths at four weeks and 26 weeks, \(95 \%\) confidenceb. \(40 \%\) humidity: Difference
In an accelerated failure test, components are operated under extreme conditions so that a substantial number will fail in a rather short time. In such a test involving two types of microchips, 600 chips manufactured by an existing process were tested, and 125 of them failed. Then 800 chips
The article "Soft Drinks Consumption Is Associated with Nonalcoholic Fatty Liver Disease Independent of Metabolic Syndrome in Chinese Population" (G. Meng, B. Zhang, et al., European Journal of Nutrition, 2017, online) presents the results of a study of soft drink and smoking habits in a sample of
The article "Bioremediation of Soil Contaminated Crude Oil by Agaricomycetes" (Mohammad-Sichani, Assadi, et al., Journal of Environmental Health and Engineering, 2017, online) describes an experiment to determine the effectiveness of mushroom compost in removing petroleum contaminants from soil.
A pit is considered "deep" if its depth is greater than \(30 \mu \mathrm{m}\). For each of the following durations, find a confidence interval of the specified level for the difference between the proportion of pits that are deep at \(40 \%\) relative humidity and the proportion of pits that are
Find a confidence interval of the specified level for the difference in proportion of deep pits for each of the following values for humidity and pairs of durations.a. \(40 \%\) humidity: Difference between proportions of deep pits at four weeks and 26 weeks, 95\% confidenceb. \(40 \%\) humidity:
To construct a confidence interval for each of the following quantities, say whether it would be better to use paired samples or independent samples.a. The mean difference in height between identical twins.b. The mean difference in weight between Great Danes and Saint Bernards.c. The mean
To construct a confidence interval for each of the following quantities, say whether it would be better to use paired samples or independent samples.a. The mean difference in weight loss between people on two different diets.b. The mean difference in weight before and after eight weeks on a certain
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