11.3.4 Let the random variables Xil, ,Xini be iid Nund2), i 1,2, and that the X,'s be independent...
---------------------------------------------------------------------------------------------------------------------------------------------------------- Reference: 11.2.3 Suppose that X. , X are iid MI, σ2) where σ (E 9t*) is the unknown parameter but μ(€ 9) is assumed known. With preassigned α ε (0. 1), derive a level α LR test for a null hypothesis Ho : σ.-a> 0) against an alternative hypothesis H, : σ2 σ1 in the implementable form. {Note: Recall from the Exercise 8.5.5 that no UMP level a test exists for testing Ho versus 8.5.5 Let X, X, be...
N.B: Solve only for (i), but draw the power function for (i) as well. X, are iid random variables from the M11, σ2) unknown, μ 01 8.3.1 Suppose that X1, population where μ is assumed known but σ is fix a number α E (0, 1) and to positive numbers σο, σ1. g, () ( : M". Wi Derive the MP level a test for Ho : σ in the simplest implementable form: (i) σ0 versus H1 : σ-01 (>...
, Xn iid. N 5. Let Xi, (μ, σ2), μ E R and σ2 > 0 are both unknown. Find an asymp- totically likelihood ratio test (LRT) of approximate size α for testing μ-σ 2 H1:ťtơ2 Ho : versus , Xn iid. N 5. Let Xi, (μ, σ2), μ E R and σ2 > 0 are both unknown. Find an asymp- totically likelihood ratio test (LRT) of approximate size α for testing μ-σ 2 H1:ťtơ2 Ho : versus
(1 point) In order to compare the means of two populations, independent random samples of 271 observations are selected from each population, with the following results: Sample 1 Sample 2 1145 2 120 (a) Use a 99 % confidence interval to estimate the difference between the population means (A-μ). (b) Test the null hypothesis: HO : (μί-12-0 versus the alternative hypothesis. Ha : (μ-μ2)メ (i) the test statistic z () the positive critical z score (ii) the negative critical z...
Independent random samples selected from two normal populations produced the sample means and standard dev atons shown to the right. a. Assuming equal variances, conduct the test Ho: (μι-μ2)-U against Ha: μι-μ2) #0 using α .10. b. Find and interpret the 90% confidence interval for(μ1-μ2) Sample 1 Sample 2 x1 59 x2-7.9 13 2-4.8 a. Find the trst statistic. The test statistic is Round to two decimal places as needed.) ind the p vaue. The p-value is Round to three...
8.4.12 Suppose that X, .., Y, are iid random variables having the ernoulli(p) distribution where p e (0, 1) is the unknown parameter. With (0, l ), derive the randomized UMP level α test for l, P-Po p reassigned oE versus H p Po where p, is a number between 0 and 1 8.4.12 Suppose that X, .., Y, are iid random variables having the ernoulli(p) distribution where p e (0, 1) is the unknown parameter. With (0, l ),...
8. Let X (i-1,2) be independent N(0,1) random variables. a. Find the value of c such that P ( (X1 + X2 )2/( X2 -X1)2 < c ) =.90 b. Find P(2 X1 -3 X2< 1.5) c. Find 95th percentile of the distribution of Y-2 X1 -3 X2
Likelihood Ratio Tests - I only require (c) and (d) here. I have posted (a) and (b) in another question Let X1,..., Xn be a random sample from the distribution with pdf { 0-1e--)e f(r μ, θ ) - 0. where E Rand 0 > 0 (a) If 0 is known but a is unknown, find a likelihood ratio test (LRT) of size a for testing Η : μ> Ho Ho Ho versus where oi a known constant (b) If...
Likelihood Ratio Tests - I only require (a) and (b) here. I'll post (c) and (d) for another question Let X1,..., Xn be a random sample from the distribution with pdf { 0-1e--)e f(r μ, θ ) - 0. where E Rand 0 > 0 (a) If 0 is known but a is unknown, find a likelihood ratio test (LRT) of size a for testing Η : μ> Ho Ho Ho versus where oi a known constant (b) If 0...
Likelihood Ratio Tests - I only require (a) and (b) here. I'll post (c) and (d) for another question Let X1,..., Xn be a random sample from the distribution with pdf { 0-1e--)e f(r μ, θ ) - 0. where E Rand 0 > 0 (a) If 0 is known but a is unknown, find a likelihood ratio test (LRT) of size a for testing Η : μ> Ho Ho Ho versus where oi a known constant (b) If 0...