Consider a random sample (X1,Y, ), dots, (X,Y) from a bivariate normal population for the variables X and Y having1unknown variances. Let μ, and μ denote the means of Xand Y respectively. Using the paired differences, derive thegeneralized likelihood ratio test for testing Ho: μ₁ = μ₂, against, H₁: μ₁ <μ2. define all steps clearly and find therejection region and compare with test statistic2. Consider a random sample (X₁, Y₁),..., (X, Yn) from a bivariate normal population for the vari-ables X and Y having unknown variances. Let μ₁ and μ2 denote the means of X and Y respectively.Using the paired differences, derive the generalized likelihood ratio test for testingHo 12 against H₁₁<μ2.

Understanding the Context and Setup You have paired observations from two variables \(X\) and…

Answered: Consider a random sample (X1,Y, ),…

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. 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…
The average American gets a haircut every 35 days. Is the average smaller for college students? The data below shows the results of a survey of 13 college students asking them how many days elapse between haircuts. Assume that the distribution of the population is normal. 39, 37, 36, 37, 36, 37, 38, 40, 33, 40, 27, 25, 41 What can be concluded at the the αα = 0.01 level of significance level of significance? For this study, we should use The null and alternative hypotheses would be: H0:H0: H1:H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 3 decimal places.) The p-value is αα Based on this, we should the null hypothesis.
The average American gets a haircut every 41 days. Is the average smaller for college students? The data below shows the results of a survey of 13 college students asking them how many days elapse between haircuts. Assume that the distribution of the population is normal. 44, 36, 30, 41, 41, 34, 41, 30, 44, 31, 36, 38, 43 What can be concluded at the the αα = 0.05 level of significance level of significance? For this study, we should use Select an answer z-test for a population proportion t-test for a population mean The null and alternative hypotheses would be: H0:H0: ? p μ Select an answer > ≠ = < H1:H1: ? μ p Select an answer ≠ = > < The test statistic ? z t = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 3 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer fail to reject accept reject the null hypothesis. Thus, the final conclusion is that ... The data suggest…
A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the difference in the two brands, an experiment is conducted using 14 of each brand. The tires are run until they wear out. The results are given in the table below. Compute a 90% confidence interval for μA−μB assuming the populations to be approximately normally distributed. You may not assume that the variances are equal. Brand A x1=35,300 kilometers s1=4900 kilometers Brand B x2=37,200 kilometers s2=6100 kilometers
A soft drink bottler is interested in the smooth operation of the machine used to fill cans. In particular, you want the standard deviation of the filling process to be less than 0.2 fluid ounces; otherwise, there will be a higher than tolerable percentage of cans that will not be completely full.Assume that the fill volume is approximately normally distributed. A random sample of 20 cans results in a variance of S ^ 2 = 0.0225 (ounces) ^ 2. The image shows the creation of a 95% confidence interval Create an upper 95% confidence interval
Researches are interested in whether or not the average fuel economy for compact cars is thesame as sedan cars. A sample of 36 compact cars and 25 sedan cars is taken.The sample of compacts returns a mean of ̄X = 38 miles per gallon and sample variance of s^2 = 25.The sample of sedans returns a sample mean ̄Y = 36 with a sample variance of s^2 = 49.Let μ 1 be the population mean of compacts and μ 2 for sedans. a. Create a 95% confidence interval for μ 1 .b. Now create a 95% confidence interval for μ 1 μ 2 .c. Say the interval from part b. contains 0. What can you say about the difference in the averagefuel economy of compact cars versus economy cars
Fred recieved an SATV (SAT verbal) score of 610. For SATV scores we know u=500 and o=100 and that they are normally distributed. Calculate Fred's z-score. Also, what percentage of the population has higher and lower than Fred's Score?
The diameter of steel rods manufactured on two different machines is being investigated. Suppose that the diameter of a rod is normally distributed, despite which machine is used to make the rod. Independent samples of n1=15 rods (from the first machine) and n2=17 rods (from the second machine) are randomly selected. The sample mean and sample variance of the first sample (of 15 rods) are xbar1=8.73, s1^2=0.34, respectively. The sample mean and sample variance of the second sample (of 17 rods) are xbar2=8.68 and s2^2=0.39, respectively. Based on these two samples, one can be 95% confident that that ratio of the two population variances, sigma1^2/sigma2^2 (i.e., the population variance of diameter of steel rods manufactured on the first machine over that on the second machine). Based on the data from these two independent random samples that we assume to arise from two normal populations, we would like to test the null hypothesis that the two population variances are the same versus the…
find a 95% confidence interval for each pair difference. Recall that a confidence interval for μi−μj can be constructed as follows. ( ̄xi− ̄xj)±t∗√MSE(1ni+1nj) TheMSE is the mean square error from the ANOVA table. The t^* is from the t-distribution with n−k degrees of freedom, where n is the total sample size and k the number of groups. Between Low and Medium levels of calcium. Between Low and High levels of calcium. Between Medium and High levels of calcium. Calcium GillRate Low 55 Low 63 Low 78 Low 85 Low 65 Low 98 Low 68 Low 84 Low 44 Low 87 Low 48 Low 86 Low 93 Low 64 Low 83 Low 79 Low 85 Low 65 Low 88 Low 47 Low 68 Low 86 Low 57 Low 53 Low 58 Low 47 Low 62 Low 64 Low 50 Low 45 Medium 38 Medium 42 Medium 63 Medium 46 Medium 55 Medium 63 Medium 36 Medium 58 Medium 73 Medium 69 Medium 55 Medium 68 Medium 63 Medium 73 Medium 45 Medium 79 Medium 41 Medium 83 Medium 60 Medium 48…
Using the t-table, find the critical value for a left-tailed test with an α = 0.05 for a sample size of 23.
The diameter of steel rods manufactured on two different machines is being investigated. Suppose that the diameter of a rod is normally distributed, despite which machine is used to make the rod. Independent samples of n1=15 rods (from the first machine) and n2=17 rods (from the second machine) are randomly selected. The sample mean and sample variance of the first sample (of 15 rods) are xbar1=8.73, s1^2=0.34, respectively. The sample mean and sample variance of the second sample (of 17 rods) are xbar2=8.68 and s2^2=0.39, respectively. Based on these two samples, one can be 95% confident that that ratio of the two population variances, sigma1^2/sigma2^2 (i.e., the population variance of diameter of steel rods manufactured on the first machine over that on the second machine), lies between [Put Answer Here] and [Put Answer Here] . Please keep three digits past the decimal point.
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

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