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.
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.
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.
otal plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 46 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.50 ml/kg for the distribution of blood plasma. (a)Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit ___ upper limit ___ margin of error ___ (b)What conditions are necessary for your calculations? (Select all that apply.) A-the distribution of volumes is uniform B-? is known C-the distribution of volumes is normal D-? is unknown E-n is large d)Find the sample size necessary for a 99% confidence level with maximal margin of error E =…
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,
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.
(b) A company produces cylindrical metal rods. The diameters of rods have a normal distribution with mean ucm and variance o' cm?. A random sample of 100 rods is taken and the diameter x, in cm, of each rod is measured. The results are summarised as Ex=52.1 and x = 27.303. (1) Calculate the mean and variance of the population of the diameters of the rods (iii) Detemine a 95% confidence interval for the mean diameter of the rods. (iv) Investigate, at the 1% significance level, whether the mean diameter of the rods is 0.512 cm.
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.
(1 point) Two independent samples have been selected, 95 observations from population 1 and 96 observations from population 2. The sample means 5.4. From previous experience with these populations, it is known that the variances are o? = 26 have been calculated to be x1 = 10.6 and x2 and o; = 21. (a) Find o answer: (b) Determine the rejection region for the test of Ho : (µ1 – µz2) = 2.03 and Ha: (µ1 – µ2) > 2.03 Use a = = 0.02. z > (c) Compute the test statistic. z = The final conclustion is A. There is not sufficient evidence to reject the null hypothesis that (u1 – H2) = 2.03. B. We can reject the null hypothesis that (u1 – H2) = 2.03 and accept that (u1 - 42) > 2.03. (d) Construct a 98 % confidence interval for (ui – µ2). < (H1 – H2) <
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.
Let ex be a random variable that represents the hemoglobin count (HC) in human blood (measured in grams per milliliter). In healthy adult females, x has a approximately normal distribution with a population mean of 14.0 and population standard deviation equal 2.3. Suppose a female patient had 10 blood test over the past year , and the sample mean HC was determined to be 15.3. With a level of significance a= 0.05, determine whether the patient's HC is higher than the population averages. Specifically do the following: write the data state null hypothesis H0 and the alternate hypothesis H1

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