8) Let X1, X25 be an i.i.d. sample from a normal distribution.(a) Suppose σ2== 100 is known. Find the rejection region for a test at level a = 0.1 of: 0 versus HA: µ = −1.5.Hoμ0Hoμ(b) Suppose 2 is unknown, and the sample variance S²Find the rejection region for the test above.=n-1Σ1(X(Xi - X) is 121.

Part (a):Test Type: Z-test (known variance)Null Hypothesis: H0:μ=0Alternative Hypothesis: HA:μ=−1-…

Answered: 8) Let X1, X25 be an i.i.d. sample from…

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 Y, represent the ith normal population with unknown mean , and unknown variance of for i=1,2. Consider independent random samples, Ya, Y2. the ith population with sample mean Y, and sample variance S² = Yin, of size n,, from (Y-₁². (a) What is the distribution of Y,? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho : 4 = o versus Ha i Pio when of is unknown and n, is small. : (e) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a.
Consider the test of hypothesis H0: mu=1150 against the alternative Ha: mu > 1150. Suppose n = 100 samples X1, ... , Xn were selected from a normal distribution with mean mu and variance 900. Determine the rejection region for this test at the level of significance alpha=0.025 Let T = (bar{X} - 1150) / (30/sqrt{n} ) where bar{X} = (X1, ... , Xn)/n is the sample mean sqrt{n} is the square root of n. Answer choice A. T > -1.645 B. T < -1.96 C. T > 1.96 D. T < -1.645
Let Y₂ represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Y₁₁, Yi2,,Yin, of size ni, from the ith population with sample mean Y, and sample variance S?=²-1₁-1(Y - Y₁². (a) What is the distribution of Y;? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho: ₁ = o versus Ha Hiio when of is unknown and n; is small. (c) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a.
Find the characteristic function of the geometric distribution given by P(X = r) = q' p, r = 0, 1, 2, ..., ∞, p + q = 1. %3D Hence find the mean and variance.
According to a researcher, the average level of mercury uptake in wading birds in Everglades has declined over the past several years. Ten years ago, the average level was 15 parts per million (ppm). Suppose we are interested in testing whether the average level today is less than 15 ppm. Describe the type I error for the test of hypothesis. O The mean mercury level is equal to 15 ppm when in fact the mean is less than 15 ppm. O The mean mercury level is less than 15 ppm when in fact the mean is equal to 15 ppm. O The mean mercury level is greater than 15 ppm when in fact the mean is equal to 15 ppm.
Let Y, represent the ith normal population with unknown mean 44, and unknown variance of for i 1,2. Consider independent random samples, Ya, Y₁2,,Yin, of size ni, from the ith population with sample mean Y, and sample variance S?=1Σj=1(Y₁j - Y₁². (a) What is the distribution of Y;? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho : μi = μio versus Ha: Pipio when of is unknown and n, is small. (c) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a.
3 For an SRS {4₁};=, from the normal distribution. ==// (Y-M) 2 fy (y;u, 0²) - 1 е värvoze Show that the sample mean I is a consistent estimator,
We collected a sample of twenty-five observations. We assumed that the observations are from a population whose values follow a normal distribution with a mean of u and a standard deviation of five. We performed a test with these hypotheses Ho: OHμ = 0 and H₂₁:μ‡0H₁0. The test statistic is the sample mean . The 5% rejection region is 1.959964> 1.959964. What is the power of this test when μ = -2 = -2? Please state the statistical power up to the fourth decimal place.
Independent random samples selected from two normal populations produced the sample means and standard deviations shown to the right. Assuming equal variances, conduct the test Ho: (uy - H2) = 0 against Ha: (H1 - H2) #0 using a = 0.10. Sample 1 Sample 2 n, = 17 n2 = 13 %3D x, = 5.3 x, = 7.6 S, = 3.9 S2 = 4.7 ... Find the test statistic. The test statistic is (Round to two decimal places as needed.) Find the p-value. The p-value is (Round to three decimal places as needed.) State the conclusion. Choose the correct answer below. O A. Do not reject Ho. There is insufficient evidence that the means differ. O B. Do not reject Ho. There is sufficient evidence that the means differ. O C. Reject Ho. There is sufficient evidence that the means differ. O D. Reject Ho. There is insufficient evidence that the means differ.
Let Y, represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size n,, from the ith population with sample mean Y, and sample variance S?=₁1(Y-₁². (h) Find the standard error of U₂ in part (g), assuming that of = 0² = 0². (i) Discuss how the distribution of Y₁ - Y₂ can be used to test the equality of the two population means, #₁1 and 12, when o=o=o² is known. (i) Define appropriate rejection regions, in terms of Y₁-Y₂, for testing Ho: #₁ = 1₂ against a two-sided alternative hypothesis at the a level of significance.
The average height X and weight Y of males in population have a bivariate normal distribution with means µX 1.80 m., µy 90.0 kgs and standard deviations Ox = 0.30 m., oy = 15.3 kgs respectively. The correlation coefficient between X and Y is p= 0.80.
Let Y, represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Ya, Y₁2, Yin, of size n,, from the ith population with sample mean Y, and sample variance S?=1 Σ₁-1 (₁-₁)². (a) What is the distribution of Y? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho: #₁ = μio versus Ha Hi Ho when of is unknown and n, is small. : (c) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a.

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