Let Y₁, Y₂, ..., Y₁ denote a random sample from a normal distribution withknown mean μ and unknown variance o².flFind the most powerful a-level test of H₁: ² = of vs. Hå: o² = 02, where0² > 08.Show that this test is equivalent to a x² test. [Hint: Recall that for Z₁, Z₂,Zn independent standard normal random variables, ₁Z² has a x2²distribution with n df.]9Is the test from part (b) uniformly most powerful (UMP) for Hå: 0² > of?

denote a random sample from a normal distribution with known mean and unknown variance .A Uniformly…

Answered: Let Y₁, 2, known mean μ and unknown…

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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Listed in the accompanying table are weights (kg) of randomly selected U.S. Army male personnel measured in 1988 (from "ANSUR I 1988") and different weights (kg) of randomly selected U.S. Army male personnel measured in 2012 (from "ANSUR II 2012"). Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) and (b). Click the icon to view the ANSUR data. a. Use a 0.05 significance level to test the claim that the mean weight of the 1988 population is less than the mean weight of the 2012 population. What are the null and alternative hypotheses? Assume that population 1 consists of the 1988 weights and population 2 consists of the 2012 weights. OA. Ho: H1 H2 B. Ho: H1 H2 H₁: H1 H2 D. Ho: H₁₂ H₁₁₂ H₁: H₁₂ The test statistic is -2.60. (Round to two decimal places as needed.). The P-value is 0.008. (Round to three decimal places as needed.) State the…
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Listed in the accompanying table are weights (kg) of randomly selected U.S. Army male personnel measured in 1988 (from "ANSUR I 1988") and different weights (kg) of randomly selected U.S. Army male personnel measured in 2012 (from "ANSUR II 2012"). Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) and (b). Click the icon to view the ANSUR data. a. Use a 0.05 significance level to test the claim that the mean weight of the 1988 population is less than the mean weight of the 2012 population. What are the null and alternative hypotheses? Assume that population 1 consists of the 1988 weights and population 2 consists of the 2012 weights. A. Ho: H1 H2 H₁₁ H₂ C. Ho H₁ =H2 H₁: H1 H2 OB. Ho: H1 H2 H₁₁₂ OD. Ho: H1 H2 ANSUR data The test statistic is . (Round to two decimal places as needed.) ANSUR II 2012 ANSUR I 1988 80.9 85.6 83.5 73.9 103.7 78.6…
An SRS of size 10 is drawn from a population that has a normal distribution. The sample has a mean of 139 and a standard deviation of 7. Give the standard error of the mean 7 , 1
Do a two-sample test for equality of means assuming unequal variances. Calculate the p-value using Excel. (a-1) Comparison of GPA for randomly chosen college juniors and seniors: x⎯⎯1x¯1 = 4.5, s1 = .20, n1 = 15, x⎯⎯2x¯2 = 4.9, s2 = .30, n2 = 15, α = .025, left-tailed test.(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.) d.f. Not attempted t-calculated Not attempted p-value Not attempted t-critical Not attempted (a-2) Based on the above data choose the correct decision. Do not reject the null hypothesis Reject the null hypothesis
I want to know the answer and detail step by step
A study tested the claim that heights of Americans and heights of Austrians have different variances with s=7.48092 cm for Americans and 7.14756 cm for Austrians. The sample sizes are n1= 145 and n2= 157. When using the F test with these data, is it correct to reason that there is no need to check for normalcy because n1 is greater than 30, and n2 is greater than 30?
2. A pet association claims that the mean annual costs of food for dogs and cats are the same. The results for samples of the two types of pets are shown in the following table. On wished to test the claim. Assume both populations follow normal distributions Dogs Cats 21 - 16 T1= 239 n2 = 18 Iz= 203 S1 = 32 82 =28 with equal variances. Which of the following formula should be used to calculate the standardized test statistic? (a) Z = (21-32)- Do lu A n2 = (E1-2)-Do (b) Z V n1+2 (c) T (1-2)-Do (21-1)a7+(n2-1)s I1 11+11タ-3 V 1'n2 (d) T = d- Do sp/Vn (e) Z
The average size of a farm in Pekan I is 185 acres. The average size of a farm in Pekan II is 100 acre. Assume that the data were obtained from two samples with standard deviations of 38 acres and 12 acres, and sample size of 8 and 9 respectively. Can it be concluded at α = 0.05 that the average size of the farms in Pekan I and Pekan II are different? (Assume equal variances)
A sample with SS=30 and a variance of s2 =10 has n=4 scores. True or False?
A researcher wants to measure average cardiovascular health of university students and compare those scores to the average scores in the general population. Assuming that population variance is known, what statistical test is most appropriate for this study? independent-samples t-test single-sample t-test z-test for sample mean related-samples t-test
If population variance o? = 49 and sample 196 then, standard error S.E.(T) will size n = be

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