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.
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.
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 =…
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.
Records for the last 15 years have shown that the average rainfall in a certain region of the country, for the month of March, to be 1.20 inches, with s = 0.45 inches. A second region had an average rainfall of 1.35 inches, with s = 0.54. estimate the difference of the true average rainfalls in those two regions as a 95% C.I. with the assumption of normal populations and unequal variances.
(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 x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is u = 7.4 new drug for arthritis has been developed. However, it is thought that this drug may change blood. Random sample of 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.8 with sample standard deviation with sample standard deviation s = 3.3. Use a 5% level of significance to test the claim that the drug has changed (either way)
(D) and (E)
Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately 2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 51 women in rural Quebec gave a sample variance s² = 3.1. Use a 5% level of significance to test the claim that the current variance is less than 5.1. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: 0² = 5.1; H₁: 0² # 5.1 O Ho: 0² = 5.1: H₁: 0² > 5.1 O Ho: 0² 0.100 O 0.050 a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value ≤ a, we reject the null hypothesis. O Since the P-value ≤ a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is insufficient evidence to conclude that the variance of age at first marriage is less than 5.1. O At the 5% level of significance,…
Scores on a certain test are normally distributed with a variance of 15. A researcher wishes to estimate the mean score by all adults on the test. Find the sample size needed to assure with 98% confidence that the sample mean will not differ from the population mean by more than 4 units.

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