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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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
A random sample of 20 newly-born baby boys showed an average weight of 7.40 pounds while a sample of 25 newly-born baby girls showed a mean weight of 6.50 pounds. If the variance of all newly-born babies are 1.25 pounds, can we say that newly-born baby boys are heavier than newly-born baby girls using the 0.05 level?
random sample of 10 subjects have weights with a standard deviation of 10.9919 kg. What is the variance of their weights? Be sure to include the appropriate units with the result.
Please note the question is: What is the distribution of the t-test statistic if m, n -----> ∞ ?
The University of Florida is interested in determining if there is a difference in the amount of money spent on food every two weeks between male and female students. They take a random sample of 20 male students (group 2) and 20 female students (group 1). They also find that xbar2 is 106 with a standard deviation of 14, and xbar1 is 146 with a standard deviation of 39. Do not assume equal variances. Find the test statistic for the difference in the amount of money spent. (Round your answer to one number after the decimal.)
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?
Let X 1 , … , X n be identically and independently distributed with population mean 9.3 and standard deviation 1.400. Let xbar be the sample mean, xbar = 1 n ∑ i = 1 n X i. Suppose n = 14. What is the mean squared error (MSE) of 0.742*xbar as an estimator for the population mean?
A certain IQ test is known to have a population mean of 100 and standard deviation of 15 in the general population. You want to test whether psychology majors have a different average IQ than the population as a whole. Assume the variance of IQ is the same for Psych majors as it is in the general population. Suppose that Psychology majors actually have an average IQ of 108. If you do a 2-tailed test at α= .05 with a sample of 56 Psychology majors, you will be able to reject the null hypothesis if the mean IQ of your sample is below [L] or above [H]. Find L and H values. Options listed below. [L] answer choices: 96.08, 98.00, 103.92, 104.08, 110.00, 111.92. [H] Answer choices: 96.08, 98.00, 103.92, 104.08, 110.00, 111.92.
You have data drawn from a normal distribution with a known variance of 16. You set up the following NHST: • Ho: data follows a N(2, 4²) • HÃ: data follows a N(µ, 4²) where µ ‡ 2. Test statistic: standardized sample mean z. Significance level set to a = .05. You then collected n = 16 data points with sample mean 1.5. (a) Find the rejection region. Draw a graph indicating the null distribution and the rejection region. (b) Find the z-value and add it to your picture in part (a). (c) Find the p-value for this data and decide whether or not to reject Ho in favor of HA.
2. The average zone of inhibition (in mm) for mouthwash L as tested by the medical technology students has been known to be 9mm. A random sample of 10 mouthwash L was tested and the test yielded an average zone of inhibition of 7.5mm with a variance of 25 mm. Is there enough reason to believe that the anti-bacterial property of the mouthwash has decreased? Test the hypothesis that the average zone of inhibition of the mouthwash is no less than 9mm using 0.05 level of significance. A. State the hypotheses. B. Determine the test statistic to use. C. Determine the level of significance, critical value, and the decision rule. D. Compute the value of the test statistic. E. Make a decision. F. Draw a conclusion.

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