Let X1, X2,., X25 be a simple random sample from a population having distri-bution N(0, o²), where o² is an unknown parameter. For the hypotheses...Ho : o < 1,H1 : o² > 1,consider the test that rejects Ho when 5 x? > c, where the constant c ischosen to have level of significance a =i=D10.05.Obtain the constant c. [Hint: The sampling distribution of z EE1 X7 isXi25): Now find c by solving max,2<1 P(E1 X? > c) = 0.05.]i=125• After we observed a simple-random sample and obtained , X? = 38 whatwill be your decision?25• Instead, if our simple random sample gave E1 X? = 36 what will be yourdecision?25i3D1

Let X1,X2,...,X25 be a simple random sample of population having distribution N(0,σ2). Here σ2 is…

Answered: Let X1, X2, . , X25 be a simple random…

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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Let X, X2,.., X, be a random sample of size n taken from a gamma 3, Show that the sampling distribution of Q= is 0 - 2 a) b) Construct a 100(1-a)% confidence interval for e. 5 c) If EX, =150 , find a 90% confidence interval for e. i-1
from each population with bivariate normal distribution, samples were taken with each size n = 4, as follows. 6 5 8 5 Population | X₁ = 10 6 9 8 Population II X₂ = (₁ 5 45, 11 10 12 11' By using a = 5% a). in population 1, test the hypothesis Ho : μ = (₁ Is this Ho rejected? 5 b). in population II, test the hypothesis Ho:μ=(₁). Is this Ho rejected? 10 c). test the hypothesis Ho: E₁ = ₂. Is this Horejected?
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For this study, we should use The null and alternative hypotheses would be: z-test for a population proportion or t-test for a population mean Ho: (p or u) (please enter a decimal) H1: (p or u) (Please enter a decimal) The test statistic z = (please show your answer to 3 decimal places.) The critical value = (Please show your answer to 3 decimal places.) The test statistic (is or is not) in the rejection region. Based on this, we should (reject or accept or fail to accept) the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly larger 50% at � = 0.05, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger 50%. The data suggest the populaton proportion is significantly larger 50% at � = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is…
b) Suppose that X₁, X2, ..., Xn denotes a random samples from a gamma distribution f(x; a, ß). i) What will be the minimal sufficient statistic for ß? Explain. ii) If a = 2, use the appropriate method to show that Y = 2₁1 Xi B is a pivotal quantity. iii) Given that a random sample of heavy machines from Polokwane factory produced the following noise levels 85.4, 86.8, 86.1, 85.3 and 84.8. Use part ii) of question 3 b) to construct a 95% confidence interval for B.
3. (Sample size determination for hypothesis testing) Suppose that X₁,..., Xn N(μ, o2) and o² is known. We would like to test We consider the test statistic Ho: μ = po, and the critical region at significance level a 1- {=; C = T = X x; x > µo + %α² H : μ > μο· B(μ') = = (a) We write ß(µ') to be the probability of type II error given the true value of µ = µ'. Prove that 0 (za + 10 = 1²). where Þ(z) = P(Z ≤ z) is the cdf of Z ~ N(0,1). 1 n = = O 2.2.d. (b) We would like to determine the sample size n so that the probability of type I error is a and the probability of type II error is ß. Using part (a), prove that 2 - ( 0¹ (²0 + zp)) ². Po - (c) Let u denote the true average tread life of a certain type of tire. Consider testing Ho : μ = 25,000 versus H₁ : μ> 25, 000 from a normal population distribution with o = 1300. Assuming the true value of μ is μ' = 24,000. What is the sample size n so that the probability of type I error is a = 0.05 and the probability of type II error is = 0.025?
a) QUESTION 3 Suppose that Y₁, Y2, ..., Yn is a random sample from a normal distribution with parameter mean 0 and variance 0, 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 Ho if Σ₁ yc, where c is a constant that solves the probability equation 0.05 = P₁Y≥ c|0 = 1). ii) What will be the value of c in part a) if n = 15.
Let X1, ..,Xn be a random sample of distribution f(x; 0)=e-(=-0), x>0, 0 elsewhere, where 0 > 0. (a) Find the mle of 0. (b) For testing Họ : 0 = 00 vs H1 : 0 > 00, find the Likelihood Ratio Test (LRT) in terms of the mle found in part (a)
A new method has been developed in the treatment of a disease. 12 randomly selected patients were treated with this method and the time until recovery was calculated as in the picture. Establish a confidence interval for the mass mean µ. (α=0.05)
A one-sample test is conducted and the APA summary is t(9)=5.02, p<.01. The effect size was r^2=0.89. How would you describe the outcomes of this hypothesis test? A. Failed to reject H0, mainly because of the large sample size B. Failed to reject H0, mainly because of the tiny effect size C. Rejected H0, mainly because of the large effect size D. Rejected H0 mainly because of the large sample size
If, in a sample of n = 25 selected from a normal population, X= 60 and S= 10, what is your statistical decision if the level of significance, a, is 0.01, the nullI hypothesis, Ho, is µ= 50, and the alternative hypothesis, H,, is µ# 50? Click here to view page 1 of the table of the critical values of t Click here to view page 2 of the table of the critical values of t. -... Determine the critical value(s). The critical value(s) is(are). (Round to four decimal places as needed. Use a comma to separate answers as needed.)
We want to use a z-test to determine if the sample mean is greater than 20 at the alpha = 0.05. What is the critical value(s)?

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