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.

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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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In the past, a chemical company produced 880 pounds of a certain type of plastic per day. Now, using a newly developed and less expensive process, the mean daily yield of plastic for the first 50 days of production is 871 pounds; the standard deviation is 21 pounds. Do the data provide sufficient evidence to indicate that the mean daily yield for the new process is less than that of the old procedure? (Use α=0.05) (a) Alternative hypothesis for the problem above is μ 871 Ομ 880 <
I have tried multiple ways to solve this but I am just not getting it! Any assisstance I will greatly appreciate.
The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM = (round to four decimals)
In the past, a chemical company produced 880 pounds of a certain type of plastic per day. Now, using a newly developed and less expensive process, the mean daily yield of plastic for the first 50 days of production is 871 pounds; the standard deviation is 21 pounds. Do the data provide sufficient evidence to indicate that the mean daily yield for the new process is less than that of the old procedure? (Use α=0.05) (c) p-value for the test above is
N= 150 observations were collected on a time series that was identified as a AR(2) time series. The following statistics were computed from the data. Mean - 45.0 Variance 15.6 Autocorrelation function (up to lag 5) r1 = 0.80, r2 = .50, rз = .26, r4 = -.10, rs = 0.08: == Estimate the parameters of the model using the method of moments.
A random sample of 11 size AA batteries for toys yield a mean of 2.98 hours with standard deviation, 1.19 hours. (a) Find the critical value, t?/2, for a 99% CI. ??/2 = (b) Find the margin of error for a 99% CI.
The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM= (round to four decimals)
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
imagine a large class where nearly everyone scores between 83.84%, with hardly any dispersion beyond this narrow range (so it would appear to have a very narrow peak). How would your describe this distribution of data in terms of kurtosis?
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.
An electrochemical engineer has manufactured a new type of fuel cell (a type of battery)which has to undergo testing to prove its duration: the time it takes to go from fullycharged to completely uncharged, under a fixed nominal load. From the computational simulation models she has, the variance of the duration is σ2 = 4 h2 (hours squared)but she wants to estimate the mean duration time μ. To achieve this she is determinedto do the tests multiple times in independent but identical conditions. Can you findwhat is the smallest number of these tests that she has to do in order for her estimatedmean duration to be within ±0.2 h tolerance of the true mean with 95% certainty
1. In the past, a chemical company produced 880 pounds of a certain type of plastic per day. Now, using a newly developed and less expensive process, the mean daily yield of plastic for the first 50 days of production is 871 pounds; the standard deviation is 21 pounds. Do the data provide sufficient evidence to indicate that the mean daily yield for the new process is less than that of the old procedure? (Use α=0.05) (d) Conclusion of the test above is Reject the null hypothesis and the mean daily yield for the new process is less than that of the old procedure. Reject the null hypothesis and the mean daily yield for the new process is not less than that of the old procedure. Do not reject the null hypothesis and the mean daily yield for the new process is less than that of the old procedure. Do not reject the null hypothesis and the mean daily yield for the new process is not less than that of the old procedure.

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