Suppose that you have molecular type with unknown atomic mass 0.You have an atomic scale with normally-distributed error of mean 0 and variance 0.5.(a) Suppose your prior on the atomic mass is N(80, 4). If the scale reads 85, what is yourposterior pdf for the atomic mass?(b) With the same prior as in part (a), compute the smallest number of measurementsneeded so that the posterior variance is less than 0.01.

Answered: Image /qna-images/answer/efafd172-fe0b-47f6-8384-4463fc068101.jpg

Answered: Suppose that you have molecular type…

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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Suppose we guess a model with four explanatory variables with 25 observations. Also, suppose that from this estimate, the sum of the residual squares is 100. If the distribution of residues conforms to the normal distribution, which of the following is the "variance of residues"?
An auto manufacturer claims that the variance of the gas mileage in a model of a hybrid vehicle is 0.16. A random sample of 30 vehicles has a variance of 0.26. At alpha = 0.05, is there enough evidence to reject the claim? Assume the population is normally distributed.
Suppose a random sample of exponential random variables X1, ..., Xn is taken. Find the meanand standard deviation of the sample mean.
From a sample of 25 observations, the estimate of the variance of the population was found to be 15.0 From another sample of 14 observations, the estimate variance was found to be 9.7 Can we accept the hypothesis that the two samples come from populations with equal variance, or must we conclude that the variance of the second population is smaller? Use the 0.01 level of significance.
Assume that the helium porosity (in percentage) of coal samples taken from anyparticular seam is normally distributed with true population variance 0.36.(a) Compute a 95% two-sided CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85. (b) How large a sample size is necessary if the width of the 95% two-sided CI is to be 0.5? (c) Compute a 98% upper one-sided CI for true average porosity of another seam based on 16 specimens with a sample average porosity of 4.56.show major intermediate steps.
A person read that the average number of hours and adult sleeps on Friday night to Saturday morning was 7.3 hours. The researcher feels that college students do not sleep 7.3 hours on average. The researcher randomly selected 17 students and found that on average they slept 8.5 hours. The standard deviation of the sample is 1.4 hours. At (alpha) = 0.01, is there enough evidence to say that college students do not sleep 7.3 hours on average? Assume that the population is approximately normally distributed. Use the critical value method and tables. A. State the hypotheses and identify the claim with the correct hypothesis. B. Find the critical value(s). C. Compute the test value. D. Make the decision. E. Summarize the results.
Consider an engine parts supplier and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are, respectively, 2.5 inches and .00075. To reduce this variance, a new machine is designed. A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s 2 = .0002 (normal distribution). In order for a cylindrical engine part to give an engine long life, the outside diameter must be between 2.43 and 2.57 inches. If σ 2 denotes the variance of the population of all outside diameters that would be produced by the new machine, test H 0: σ 2 = .00075 versus H a: σ 2 < .00075 by setting α = .05.
The university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks which require comparable processing time to those of computer 2. A random sample of 10 processing times from computer 1 showed a mean of 51 seconds with a standard deviation of 20 seconds, while a random sample of 9 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 60 seconds with a standard deviation of 15 seconds. Assume that the populations of processing times are normally distributed for each of the two computers, and that the variances are equal. Can we conclude, at the 0.01 level of significance, that the mean processing time of computer 1, μ1, is less than the mean processing time of computer 2, μ2? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
a sample of 64 measurements are randomly selected from a poulation with a mean of 30 and a standard deviation of 5. Find the (a) mean, (b) variance, and (c) standard deviation.
The average number of pounds of sliced ham ordered per customer at the deli where Dennis used to work was 1.4, but at his new job, the average of the 32 people who have ordered ham so far is 1.5 pounds, with a standard deviation of 0.3 pounds. a) Write the null and alternative hypotheses to test if the average amount of ham bought is higher at the new store. H0:μ= H1:μ> b) For α=0.025, find the rejection region in terms of z. [Write your answer with 2 decimal places.] R:z≥ c) What test statistic corresponds to an x¯ of 1.5 pounds? [Round your answer to 2 decimal places.] z= d) Should you reject the null hypothesis?
A university wants to investigate 'low-performance' modules - where low-performance is defined as a module with an average final mark lower than 50 in a given year. To test whether ECO242 is a 'low-performance' module, a researcher gathers data on final marks for 31 first ECO242 students from past years. If the mean and variance of this sample is estimated, respectively, as 48 and 38, test the hypothesis, at α=0.05, that the true mean is 50 against the hypothesis that it is less than 50. Q1: Is this an example of (two/left/right) tailed test?

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