a)QUESTION 3Suppose that Y₁, Y2, ..., Yn is a random sample from a normal distribution with parameter mean0 and variance 0, say N(0,0). If Mr Masela and Mr Sepuru desire to use 5% level ofsignificance to test the null hypothesis Ho: 0 = 1 against alternative hypothesis H₁:0 > 1.i) Show that the uniformly most powerful test of their hypothesis rejects Ho ifΣ₁ yc, where c is a constant that solves the probability equation0.05 = P₁Y≥ c|0 = 1).ii) What will be the value of c in part a) if n = 15.

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Answered: a) Suppose that Y₁, Y₂, ..., Yn is a…

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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6. To test the null hypothesis H0: µ ≥ 25. A sample of 20, sample mean is 23, sample variance is 16. The test will be used is: Select one: Left-tail t- test Two tails t-test Right-tail t-test Right-tail z test
b) Suppose that Y₁, Y₂,..., Y₁0 is a random sample from a bernoulli (P) distribution. It is desired that the null hypothesis Ho: P = 0.5 against the alternative hypothesis H₁: P = 0.1 at a level of significance. If Ho is rejected when Σı Y = 1. i) Determine the level of significance. ii) Find the power of the test.
6.STATISTICAL INFERENCEQuestion 3 a i)
A sample of n=18n=18 data values randomly collected from a normally distributed population has variance s2=24.6s2=24.6. We wish to test the null hypothesis H0:σ2=64H0:σ2=64 against the alternative hypothesis H1:σ2<64H1:σ2<64 at a significance of α=0.01α=0.01. What is the value of the test statistic? Write your answer rounded to 3 decimal places. What is the critical value? Write your answer rounded to 3 decimal places.
Two independent samples are selected at random from two normal populations, where the unknown population variances are assumed to be equal. The sample statistics are as follows: n₁=20,x=40,s=18,n₂=10x₂=34 and $₂=16. Assume that a two-tailed hypothesis test is conducted at α = .05, what is the upper critical value? a. t = 2.0484 b. z = 1.96 c. t = 1.7011 d. z = 1.65 e. t = 1.562
I dont understand what my professor is asking me to do here...
A company that manufactures aerospace parts is considering the possibility of investing in CMU (Cellular Manufacturing Unit). Top Management desires a good estimates distribution characteristic for the FW. There are three random variables i.e., they have uncertainties in their values. An economic analyst is hired to estimate the desired parameters and FW. He concludes that the scenario presented to him is suitable for Monto Carlo simulation because there are uncertainties in three variables and the direct analytical approach is impossible. The company has done a preliminary economic analysis of the situation and provided the analyst with the following estimates: Capital Investment Normally distributed with mean of $150,000 and standard deviation of $12,000 Useful Life Uniformly distributed with a minimum of 5 years and maximum 10 years Market value $25,000 (single outcome) Annual net cash flow $15,000 probability 0.9 $20,000 probability 0.5 $25,000 probability…
A two-sample study for the difference between two population means will utilize t-test procedures and is to be done at the 0.05 level of significance. The sample sizes are 23 and 27. The variances are 18 and 36, respectively. What is the upper critical value t, for the rejection region if:(a) the alternative hypothesis is one-sided, and you assume that the population variances are vunequal?(b) the alternative hypothesis is two-sided , and you assume that the population variances are unequal?(c) the alternative hypothesis is one-sided and you assume that the population variances are equal?(d) the alternative hypothesis is two-sided, and you assume that the population variances are equal?
In order to compare the means of two normal populations that are known to have equal variances, independent random samples are taken of sizes n1 = 10 and n2 data yield: = 15. The results from the sample Sample 1 Sample 2 sample mean = 52 sample mean = 45 S1 5 S2 = 3 Sp 3.9065 %3D To test the null hypothesis Ho: H1 - H2=0 versus the alternative hypothesis H,: µ1 -µ2> 0 at the 0.01 level of significance, the most accurate statement is O The value of the test statistic is -8.48 and the critical value is -2.5 O The value of the test statistic is 4.39 and the critical value is 1.96 O The value of the test statistic is -4.39 and the critical value is -1.96 The value of the test statistic is 3.79 and the critical value is 2.326 The value of the test statistic is 8.48 and the critical value is +2,50
a) Suppose that Y₁, Y₂, ..., Y₁ is a random sample from a normal distribution with parameter mean 0 and variance e, say N(0,0). If Mr Masela and Mr Sepuru desire to use 5% level of significance to test the null hypothesis Ho: 0 = 1 against alternative hypothesis H₁:0 > 1. i) Show that the uniformly most powerful test of their hypothesis rejects H, if Σyc, where c is a constant that solves the probability equation 0.05=PY≥c|0 = 1). ii) What will be the value of c in part a) if n = 15. b) An academic Professor conducted a research aimed at exploring the experience and challenges faced by people who are diagnosed with dementia and their families. If the professor perform a hypothesis test to decide whether the mean age of all people diagnosis with initial occurrence of dementia is less than 55 years old. Based on the statement, explain, what each of the following would mean. i) Type I error. ii) Correct decision. iii) Type II error. c) Suppose that the results of carrying out the…

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