Q3: The effective life of a component used in a jet-turbine aircraft engine is a random variable with mean5000 hours and standard deviation 40 hours. The distribution of effective life is fairly close to a normalcomponent that increases the mean life to 5030 hours and decreases the standard deviation to 30 hours.distribution. The engine manufacturer introduces an improvement into the manufacturing process for thisSuppose that a random sample of n₁ = 16 components is selected from the "Old" process and a randomsample of n₂ = 25 components is selected from the "Improved" process.What is the probability that difference in the two-sample meansthat the old and improved processes can be regarded as independent populations.5X₂X₁ is at least 15 hours? Assume

The effective life of a component used in a jet-turbine aircraft engine is a random variable with…

Answered: Q3: The effective life of a component…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A medical team was asked to study the difference in systolic blood pressure (BP) between men (µ1) and women (µ2) with heart trouble. The BP measurements are normally distributed. The variance of the men’s group is equal to that of the women’s group. For a random sample of 4 men, thesample average is 175 and the sample standard deviation is 16. For a random sample of 5 women, the sample average is 145 and the sample standard deviation is 12. What is the 95% confidence interval estimate for the difference between the two means? 8.02 to 51.98 5.05 to 34.05 −4.20 to 33.20 −0.65 to 29.65
An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).
If X is a normally distributed random variable with a mean of 235 Findthe standard deviation given ?(? > 250) = 0.37 .
The sample mean and standard deviation from a random sample of 29 observations from a normal population were computed as ?¯=23x¯=23 and s = 6. Calculate the t statistic of the test required to determine whether there is enough evidence to infer that the population mean is greater than 21. Test Statistic =
Students in Mr Brawn's exercise class have to do press-ups and sit-ups. The number of press-ups x and the number of sit-ups y done by a random sample of 8 students are summarised below. Σχy = 11 222, Σε = 272, Σy = 320, Σχ" = 10 164, Σy = 13 464. The addition of the mean and standard deviation of the number of press-ups done by these students, is (A) 44 (B) 44.07 (C) 44.70 (D)None of these * Q3
A sample is selected from a population withu = 50. After a treatment is administered to the 16 individuals in the sample, the mean is found to be M = 55 and the standard deviation is s = 8, What is the test statistic for the sample mean?
The time necessary to complete the technical interview for the Google intership is normally distributed with a mean of sixty-three minutes, and a standard deviation of twelve minutes. Let the random variable X represent the number of minutes a randomly chosen student takes to complete the assessment. If a sample of three dozen students is taken, what is the standard deviation of the sample mean σX¯ and what is the probability that the sample mean would be 59 minutes or fewer?
At the alpha = 0.01 level , what is the correct conclusion for this test? The daily temperatures in fall and winter months in Virginia have a mean of 62F. A meteorologist in southwest Virginia believes the mean temperature is colder in this area. The meteorologist takes a random sample of 30 daily temperatures from the fall and winter months over the last five years in southwest Virginia. The mean temperature for the sample is 59 degrees * F with a standard deviation of 6.21 degrees * F The meteorologist conducts a one -sample t-test for and calculates a P value of 0.007. The meteorologist should reject the null hypothesis since 0.007 < 0.01 . There is convincing evidence that the mean temperature in fall and winter months in southwest Virginia is less than 62 F. The meteorologist should reject the null hypothesis since 0.007 < 0.01 . There is not convincing evidence that the mean temperature in fall and winter months in southwest Virginia is less than 62 F. The meteorologist…
Suppose that three drugs used to reduce systolic blood pressure are compared in a randomized experiment in which four people use each drug for a month. The data for the reductions in systolic blood pressure for the N = 12 participants follow. Drug 1 Drug 2 Drug 3 7 8 16 2 12 5 5 6 4 10 Calculate the F-statistic for comparing the mean cholesterol reductions for the three drugs. What is the value of F? | (report to 2 decimal places) What are the degrees of freedom for this statistic - Between df? .Within df?
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5 c.)
Two companies manufacture a rubber material intended for use in an automotive application. The part will be subjected to abrasive wear in the field application, so we decide to compare the material produced by each company in a test. A random sample of 35 samples of material from each company are tested in an abrasion test and the amount of wear after 1000 cycles is observed. For company 1, the sample mean of wear is X1 = 22 mg/ 1000 cycles and sample standard deviation of wear is S1 = 3 mg/ 1000 cycles, while for company 2, we obtain X, = 25 mg/ 1000 cycles and sample standard deviation of wear is S, = 9 mg/ 1000 %3D cycles. Test the hypothesis that the two companies produce material with different mean wear. Use a = 0.01. (1) Critical Region: or z > (Give your answer to 3 decimal places.) (ii) Test Statistic: z = (Give your answer to 3 decimal places.) (iii) Do we reject or fail to reject the null hypothesis? OReject H, OFail to reject Ho

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