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statistics for engineers and scientists

Questions and Answers of Statistics For Engineers And Scientists

The median age for people in the study is 10.82 years. What proportion of those older than 10.82 years have asthma? What proportion of those 10.82 years or younger have asthma? Do these proportions
The median age for people in the study is 10.82 years. Using only those individuals over the age of 10.82 , perform a test of the null hypothesis that the mean FEV1 for those with asthma is equal to
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 study is 10.82 years. Using only those individuals over the
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,
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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 \(70 \%\)
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,
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
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
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
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
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
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.
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
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
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,
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:
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:
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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,
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
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%
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, \(99 \%\)
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
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.
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
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
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
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
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
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 \(10^{-8} \mathrm{~m} / \mathrm{s}^{2}\).
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)
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
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
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,
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
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
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
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
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
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
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
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
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 \(75 \%\)
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
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
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
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
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

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