Find the minimum sufficient statistic in the following situations. In order to establish minimality, whenthis is not obvious, consider the ratio L(0; y)/L(e; z) for two data sets y and z. What is the minimalrequirement on y and z to have in common, for this ratio to be free of parameters?1) A sample from a uniform distribution on the interval (0 – 1/2, 0 + 1/2)2) A simple linear regression model, under normality, with x-values fixed.

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Answered: Find the minimum sufficient statistic…

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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given normally distributed sample x=12 and s=3, use the Empirical Rule determine the upper and lower bounds to contain approximately 95% of your data
Find the critical value of t for a t-distribution with 30 degrees of freedom such that the area between −t and t is 99%.
Find the t values that form the boundary of the critical region in the right-hand tail for a one tailed test with α=.01 for each of the following sample sizes: A) n=10 B) n=20 c) n=30
Let X1,...,Xn be an iid sample from f(x | θ) = θ xθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ
Let X1, . . . , Xn be an iid sample from f(x | θ) = θxθ−1 , 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ.
The following data were obtained from a two-factor independent-measures experiment with n=10 participants in each treatment condition. B1 B2 A1 M=4 T=50 SS=20 M=7 T=20 SS=28 A2 M=1 T=20 SS=12 M=4 T=30 SS-20 a. Calculate degrees of freedom and locate the critical region for each of the three tests (a=.05) b. Calculate the three F-ratios c. State the conclusion for each test.
Which of the following correctly compares the tt-distribution and zz-distribution? A. For small sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric. B. For large sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric. C. The curves of both distributions are symmetric, but the height of the density curve of the t-distribution is taller than the height of the density curve of the z-distribution. D. The area under the density curve of the t-distribution is greater than the area under the density curve of the z-distribution, especially for small sample sizes. E. The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes.
Find the critical value of t a/2 that corresponds to a degree of confidence of 90% and a sample size of 8.
With reference to the uniform population of Exam-ple 4, use the definition of consistency to show that Yn, the nth order statistic, is a consistent estimator of theparameter β.
For a Student’s t-distribution with mean 0, standard deviation 1, and degrees of freedom 49, which of the following Python lines outputs the critical value a if ? Note: a is a constant. Select one. A import scipy.stats as stprint(st.t.ppf(0.135, 49, 0, 1)) B import scipy.stats as stprint(st.t.pdf(0.135, 49, 0, 1)) C import scipy.stats as stprint(st.t.sf(0.135, 49, 0, 1)) D import scipy.stats as stprint(st.t.cdf(0.135, 49, 0, 1))
Find the t value that forms the boundary of the critical region in the right-hand tail for a one-tailed test with α = .01 for each of the following sample sizes. n = 10 n = 20 n = 30
For the given data use the kruskal wallis test, (a) determine the test statistic H,(b) determine the critical value at the α=0.05level of significance, and(c) test whether the distributions of the populations are different.

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