All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Hire a Tutor
AI Study Help New

Search
Sign In
Register

study help
business
introduction to probability statistics

Questions and Answers of Introduction To Probability Statistics

Ten bearings made by a certain process have a mean diameter of \(0.5060 \mathrm{~cm}\) and a standard deviation of \(0.0040 \mathrm{~cm}\). Assuming that the data may be looked upon as a random
The freshness of produce at a mega-store is rated a scale of 1 to 5 , with 5 being very fresh. From a random sample of 36 customers, the average score was 3.5 with a standard deviation of 0.8.(a)
A café records that in \(n=81\) cases, the coffee beans for the coffee machine lasted an average of 225 cups with a standard deviation of 22 cups.(a) Obtain a 90\% confidence interval for \(\mu\),
In an air-pollution study performed at an experiment station, the following amount of suspended benzenesoluble organic matter (in micrograms per cubic meter) was obtained for eight different samples
Modify the formula for \(E\) on page 216 so that it applies to large samples which constitute substantial portions of finite populations, and use the resulting formula for the following problems:(a)
Instead of the large sample confidence interval formula for \(\mu\) on page 230, we could have given the alternative formula\[\bar{x}-z_{\alpha / 3} \cdot \frac{\sigma}{\sqrt{n}}Explain why the one
Suppose that we observe a random variable having the binomial distribution. Let \(X\) be the number of successes in \(n\) trials.(a) Show that \(\frac{X}{n}\) is an unbiased estimate of the binomial
The statistical program MINITAB will calculate the small sample confidence interval for \(\mu\). With the nanopillar height data in \(\mathrm{C} 1\),produces the output(a) Obtain a \(90 \%\)
You can simulate the coverage of the small sample confidence intervals for \(\mu\) by generating 20 samples of size 10 from a normal distribution with \(\mu=20\) and \(\sigma=5\) and computing the
Refer to Example 13, Chapter 3, where 294 out of 300 ceramic insulators were able to survive a thermal shock.(a) Obtain the maximum likelihood estimate of the probability that a ceramic insulator
Refer to Example 7, Chapter 10, where 48 of 60 transceivers passed inspection.(a) Obtain the maximum likelihood estimate of the probability that a transceiver will pass inspection.(b) Obtain the
The daily number of accidental disconnects with a server follows a Poisson distribution. On five days\[\begin{array}{lllll}2 & 5 & 3 & 3 & 7\end{array}\]accidental disconnects are observed.(a) Obtain
In one area along the interstate, the number of dropped wireless phone connections per call follows a Poisson distribution. From four calls, the number of dropped connections is\[\begin{array}{llll}2
Refer to Exercise 7.12.(a) Obtain the maximum likelihood estimates of \(\mu\) and \(\sigma\).(b) Find the maximum likelihood of the probability that the next run will have a production greater than
Refer to Exercise 7.14.(a) Obtain the maximum likelihood estimates of \(\mu\) and \(\sigma\).(b) Find the maximum likelihood of the coefficient of variation \(\sigma / \mu\).Data From Exercises
Find the maximum likelihood estimator of \(p\) when\[f(x ; p)=p^{x}(1-p)^{1-x} \quad \text { for } \quad x=0,1\]
Let \(x_{1}, \ldots, x_{n}\) be the observed values of a random sample of size \(n\) from the exponential distribution \(f(x ; \beta)=\beta^{-1} e^{-x / \beta}\) for \(x>0\).(a) Find the maximum
Let \(X\) have the negative binomial distribution\(f(x)=\left(\begin{array}{l}x-1 \\ r-1\end{array}\right) p^{r}(1-p)^{x-r}\) for \(x=r, r+1, \ldots\)(a) Obtain the maximum likelihood estimator of
A civil engineer wants to establish that the average time to construct a new two-storey building is less than 6 months.(a) Formulate the null and alternative hypotheses.(b) What error could be made
A manufacturer of four-speed clutches for automobiles claims that the clutch will not fail until after 50,000 miles.(a) Interpreting this as a statement about the mean, formulate a null and
An airline claims that the typical flying time between two cities is 56 minutes.(a) Formulate a test of hypotheses with the intent of establishing that the population mean flying time is different
A manufacturer wants to establish that the mean life of a gear when used in a crusher is over 55 days. The data will consist of how long gears in 80 different crushers have lasted.(a) Formulate the
A statistical test of hypotheses includes the step of setting a maximum for the probability of falsely rejecting the null hypothesis. Engineers make many measurements on critical bridge components to
Suppose you are scheduled to ride a space vehicle that will orbit the earth and return. A statistical test of hypotheses includes the step of setting a maximum for the probability of falsely
Suppose that an engineering firm is asked to check the safety of a dam. What type of error would it commit if it erroneously rejects the null hypothesis that the dam is safe? What type of error would
Suppose that we want to test the null hypothesis that an antipollution device for cars is effective. Explain under what conditions we would commit a Type I error and under what conditions we would
If the criterion on page 242 is modified so that the manufacturer's claim is accepted for \(\bar{X}>1640\) cycles, find(a) the probability of a Type I error;(b) the probability of a Type II error
Suppose that in the electric car battery example on page 242, \(n\) is changed from 36 to 50 while everything else remains the same. Find(a) the probability of a Type I error;(b) the probability of a
It is desired to test the null hypothesis \(\mu=30\) minutes against the alternative hypothesis \(\mu
Several square inches of gold leaf are required in the manufacture of a high-end component. Suppose that, the population of the amount of gold leaf has \(\sigma=8.4\) square inches. We want to test
A producer of extruded plastic products finds that his mean daily inventory is 1,250 pieces. A new marketing policy has been put into effect and it is desired to test the null hypothesis that the
Specify the null and alternative hypotheses in each of the following cases.(a) A car manufacturer wants to establish the fact that in case of an accident, the installed safety gadgets saved the lives
Refer to Exercise 7.1 where a construction engineer recorded the quantity of gravel (in metric tons) used in concrete mixes. The quantity of gravel for \(n=24\) sites has \(\bar{x}=5,818\) tons and
Refer to data in Exercise 7.3 on the labor time required to produce an order of automobile mufflers using a heavy stamping machine. The times (hours) for \(n=52\) orders of different parts has
Refer to Exercise 7.5, where the number of unremovable defects, for each of \(n=45\) displays, has \(\bar{x}=\) 2.467 and \(s=3.057\) unremovable defects.(a) Conduct a test of hypotheses with the
Refer to Exercise 7.12, where, in a pilot process, vertical spirals were cut to produce latex from \(n=8\) trees to yield (in liters) in a week.26.8 32.5 29.7 24.6 31.5
Refer to Exercise 7.14, where \(n=9\) measurements were made on a key performance indicator.\[\begin{array}{lllllllll}123 & 106 & 114 & 128 & 113 & 109 & 120 & 102 &
Refer to Exercise 7.22, where, in \(n=81\) cases, the coffee machine needed to be refilled with beans after 225 cups with a standard deviation of 22 cups.(a) Conduct a test of hypotheses with the
Refer to Exercise 2.34, page 46, concerning the number of board failures for \(n=32\) integrated circuits. A computer calculation gives \(\bar{x}=7.6563\) and \(s=\) 5.2216. At the 0.01 level of
In 64 randomly selected hours of production, the mean and the standard deviation of the number of acceptable pieces produced by a automatic stamping machine are \(\bar{x}=1,038\) and \(s=146\). At
With reference to the thickness measurements in Exercise 2.41 , test the null hypothesis that \(\mu=30.0\) versus a two-sided alternative. Take \(\alpha=0.05\).Data From Exercise 2.41 2.41 The
A random sample of 6 steel beams has a mean compressive strength of 58,392 psi (pounds per square inch) with a standard deviation of 648 psi. Use this information and the level of significance
A manufacturer claims that the average tar content of a certain kind of cigarette is \(\mu=14.0\). In an attempt to show that it differs from this value, five measurements are made of the tar content
The statistical program MINITAB will calculate \(t\) tests. With the nanopillar height data in \(\mathrm{C} 1\),You must compare your preselected \(\alpha\) with the printed \(P\)-value in order to
Refer to the nanopillar height data on page 25. Using the \(95 \%\) confidence interval, based on the \(t\) distribution, for the mean nanopillar height(a) decide whether or not to reject \(H_{0}:
Repeat Exercise 7.66 but replace the \(t\) test with the large sample \(Z\) test.Data From Exercise 7.66 7.66 Refer to the nanopillar height data on page 25. Using the 95% confidence interval,
Refer to the green gas data on page 241 . Using the \(95 \%\) confidence interval, based on the \(t\) distribution for the mean yield(a) decide whether or not to reject \(H_{0}: \mu=5.5
Refer to the labor time data in Exercise 7.3. Using the \(90 \%\) confidence interval, based on the \(t\) distribution, for the mean labor time(a) decide whether or not to reject \(H_{0}: \mu=1.6\)
Repeat Exercise 7.69 but replace the \(t\) test with the large sample \(Z\) test.Data From Exercise 7.69 7.69 Refer to the labor time data in Exercise 7.3. Using the 90% confidence interval,
Refer to the example concerning average sound intensity on page 260 . Calculate the power at \(\mu_{1}=77\) when(a) the level is changed to \(\alpha=0.03\).(b) \(\alpha=0.05\) but the alternative is
MINITAB calculation of power These calculations pertain to normal populations with known variance and provide an accurate approximation in the large sample case where \(\sigma\) is unknown. To
Use computer software to repeat Exercise 7.71.Data From Exercise 7.71 77 7.71 Refer to the example concerning average sound inten- sity on page 260. Calculate the power at when (a) the level is
MINITAB calculation of sample size Refer to Exercise 7.72, but this time leave Sample size blank but Type 0.90 in power to obtain the partial output concerning sample sizeRefer to the example
MINITAB calculation of power or OC curve Refer to the steps in Exercise 7.72, but enter a range of values for the difference.Here 0:3/.1 goes in steps from 0 to 3 in steps of . 1 for Example 22.With
Specify the null hypothesis and the alternative hypothesis in each of the following cases.(a) An engineer hopes to establish that an additive will increase the viscosity of an oil.(b) An electrical
With reference to Example 7 on page 29, find a 95% confidence interval for the mean strength of the aluminum alloy.Data From Example 7 EXAMPLE 7 A two sample t test to show a difference in strength
While performing a certain task under simulated weightlessness, the pulse rate of 32 astronaut trainees increased on the average by 26.4 beats per minute with a standard deviation of 4.28 beats per
It is desired to estimate the mean number of hours of continuous use until a printer overheats. If it can be assumed that \(\sigma=4\) hours, how large a sample is needed so that one will be able to
A sample of 15 pneumatic thermostats intended for use in a centralized heating unit has an average output pressure of \(9 \mathrm{psi}\) and a standard deviation of \(1.5 \mathrm{psi}\). Assuming the
In order to test the durability of a new paint, a highway department had test strips painted across heavily traveled roads in 15 different locations. If on the average the test strips disappeared
Referring to Exercise 7.82 and using 14,380 as an estimate of \(\sigma\), find the sample size that would have been needed to be able to assert with \(95 \%\) confidence that the sample mean is off
A laboratory technician is timed 20 times in the performance of a task, getting \(\bar{x}=7.9\) and \(s=1.2 \mathrm{~min}-\) utes. If the probability of a Type I error is to be at most 0.05 , does
In a fatigue study, the time spent working by employees in a factory was observed. The ten readings (in hours) were\[\begin{array}{llllllllll}4.8 & 3.6 & 10.8 & 5.7 & 8.2 & 6.8 & 7.5 & 7.7 & 6.3 &
An industrial engineer concerned with service at a large medical clinic recorded the duration of time from the time a patient called until a doctor or nurse returned the call. A sample of size 180
Refer to Exercise 7.87.(a) Perform a test with the intention of establishing that the mean time to return a call is greater than 1.5 hours. Use \(\alpha=0.05\).(b) In light of your conclusion in part
The compressive strength of parts made from a composite material are known to be nearly normally distributed. A scientist, using the testing device for the first time, obtains the tensile strength
Refer to Exercise 2.58, where \(n_{1}=30\) specimens of \(2 \times 4\) lumber have \(\bar{x}=1,908.8\) and \(s_{1}=327.1\) psi. A second sample of size \(n_{2}=40\) specimens of larger dimension, \(2
Refer to Exercise 8.1 and obtain a \(95 \%\) confidence interval for the difference in mean tensile strength.Data From Exercise 8.1 Data From Exercise 2.58 8.1 Refer to Exercise 2.58, where n = 30
The dynamic modulus of concrete is obtained for two different concrete mixes. For the first mix, \(n_{1}=33\), \(\bar{x}=115.1\), and \(s_{1}=0.47\) psi. For the second mix, \(n_{2}=31,
Refer to Exercise 8.3 and obtain a \(95 \%\) confidence interval for the difference in mean dynamic modulus.Data From Exercise 8.3 8.3 The dynamic modulus of concrete is obtained for two different
An investigation of two types of bulldozers showed that 50 failures of one type of bulldozer took on an average 6.8 hours to repair with a standard deviation of 0.85 hours, while 50 failures of the
Studying the flow of traffic at two busy intersections between 4 P.M. and 6 P.M. (to determine the possible need for turn signals), it was found that on 40 weekdays there were on the average 247.3
Given the \(n_{1}=3\) and \(n_{2}=2\) observations from Population 1 and Population 2, respectively,(a) Calculate the three deviations \(x-\bar{x}\) and two deviations \(y-\bar{y}\).(b) Use your
Two methods for manufacturing a product are to be compared. Given 12 units, six are manufactured using method \(M\) and six are manufactured using method \(N\).(a) How would you assign manufacturing
Measuring specimens of nylon yarn taken from two spinning machines, it was found that 8 specimens from the first machine had a mean denier of 9.67 with a standard deviation of 1.81 , while 10
We know that silk fibers are very tough but in short supply. Breakthroughs by one research group result in the summary statistics for the stress \((\mathrm{MPa})\) of synthetic silk fibers (Source:
The following are the number of hydraulic pumps which a sample of 10 industrial machines of Type \(A\) and a sample of 8 industrial machines of Type \(B\) manufactured over a certain fixed period of
With reference to Example 5 construct a 95% confidence interval for the true difference between the average resistance of the two kinds of wire.Data From Example 5 EXAMPLE 5 The multiplication rule
In each of the parts below, first decide whether or not to use the pooled estimator of variance. Assume that the populations are normal.(a) The following are the Brinell hardness values obtained for
A civil engineer wants to compare two machines for grinding cement and sand. A sample of a fixed quantity of cement and sand is taken and put in each machine. The machines are run and the fineness of
Refer to Exercise 8.14. Test with \(\alpha=0.01\), that the mean difference is 0 versus a two-sided alternative.Data From Exercise 8.14Find a 99% confidence interval for the mean difference in
The following data were obtained in an experiment designed to check whether there is a systematic difference in the weights obtained with two different scales:Use the paired \(t\) test at the 0.05
Refer to Example 14 concerning suspended solids in effluent from a treatment plant. Take the square root of each of the measurements and then take the difference.(a) Construct a \(95 \%\) confidence
Refer to Example 14 concerning suspended solids in effluent from a treatment plant. Take the natural logarithm of each of the measurements and then take the difference.(a) Construct a 95% confidence
A shoe manufacturer wants potential customers to compare two types of shoes, one made of the current PVC material \(X\) and one made of a new PVC material \(Y\). Shoes made of both are available.
Referring to Example 13, conduct a test to show that the mean change \(\mu_{D}\) is different from 0 . Take \(\alpha=0.05\).Data From Example 13 EXAMPLE 13 The chi square test of independence To
In a study of the effectiveness of physical exercise in weight reduction, a group of 16 persons engaged in a prescribed program of physical exercise for one month showed the following results:Use the
An engineer wants to compare two busy hydraulic belts by recording the number of finished goods that are successfully transferred by the belts in a day. Describe how to select 3 of the next 6 working
An electrical engineer has developed a modified circuit board for elevators. Suppose 3 modified circuit boards and 6 elevators are available for a comparative test of the old versus the modified
It takes an average of 30 classes for an instructor to teach a civil engineering student probability. The instructor introduces a new software which they feel will lead to faster calculations. The
How would you randomize, for a two sample test, if 50 cars are available for an emissions study and you want to compare a modified air pollution device with that used in current production?
With reference to Exercise 2.64, test that the mean charge of the electron is the same for both tubes. Use \(\alpha=0.05\).Data From Exercise 2.64 2.64 J. J. Thomson (1856-1940) discovered the
Two adhesives for pasting plywood boards are to be compared. 10 tubes are prepared using Adhesive I and 8 tubes are prepared using Adhesive II. Then 18 different pairs of plywood boards are pasted
With reference to Example 2, Chapter 2, test that the mean copper content is the same for both heats.Data From Example 2Data From Figure 3.2 EXAMPLE 2 Relation of regions in Venn diagrams to events
Random samples are taken from two normal populations with \(\sigma_{1}=9.6\) and \(\sigma_{2}=13.2\) to test the null hypothesis \(\mu_{1}-\mu_{2}=41.2\) against the alternative hypothesis
With reference to Example 8, find a \(90 \%\) confidence interval for the difference of mean strengths of the alloys(a) using the pooled procedure;(b) using the large samples procedure.Data From
How would you randomize, for a two sample test, in each of the following cases?(a) Forty combustion engines are available for a speed test and you want to compare a modified exhaust valve with the
With reference to part(a) of Exercise 8.33, how would you pair and then randomize for a paired test?Data From Exercise 8.33 8.33 How would you randomize, for a two sample test, in each of the
Two samples in \(\mathrm{C} 1\) and \(\mathrm{C} 2\) can be analyzed using the MINITAB commandsIf you do not click Assume equal variances, the Smith-Satterthwaite test is performed.The output
Refer to Example 13 concerning an array of sites that smell toxic chemicals. When exposed to the common manufacturing chemical Arsine, a product of arsenic and acid, the change in the red component

Showing 6100 - 6200 of 7137

First
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
Last

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved