Let Y, represent the ith normal population with unknown mean 44, and unknown varianceof for i 1,2. Consider independent random samples, Ya, Y₁2,,Yin, of size ni, fromthe 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 versusHa: 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 probabilitystatement for the level of significance, a.

Write the distribution of Yi bar and state its all the relevant parametersWrite the distribution of…

Answered: m-1 j=) t is the distribution of 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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26 The table to the right shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At α=0.01, can you conclude that the mean costs per ounce are different? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. Very good stain removal Good stain removal Fair stain removal 0.37 0.75 0.60 0.49 2.66 1.18 0.33 0.46 0.46 1.64 0.33 0.50 0.58 0.41 1.39 (b) Identify the degrees of freedom for the numerator and for the denominator, determine the critical value, and determine the rejection region. The degrees of freedom for the numerator, d.f.N, is ____ and the degrees of freedom for the denominator, d.f.D, is _____ The critical…
Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.t Over a period of months, an adult male patient has taken seven blood tests for uric acid. The mean concentration was x = 5.29 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with o = 1.95 mg/dl. (a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. 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.) On is large O o is known O o is unknown O normal distribution of uric acid O uniform distribution of uric acid (c) Interpret your results in the context of this problem. O we are 95% confident that the true uric acid level for this patient falls within this interval. O we are 5% confident that…
Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 5.4 and standard deviation ? = 0.6. a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.) _______ < z b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.) z < ______ c) Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.) ________ < z < _______
The height of an 8th grader is modeled using the normal distribution shown below. The mean of the distribution is 59.1 in and the standard deviation is 1.2 in. In the figure, Vis a number along the axis and is under the highest part of the curve. And, U and W are numbers along the axis that are each the same distance away from V. Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of U, V, and W. Percentage of total area shaded: (Choose one) V 56 58 60 62 Height (in inches)
A person's body mass index (BMI) is computed by dividing the weight (kg) by the square of height (m). The accompanying table contains the BMI statistics for random samples of males and females. Assume that the two samples are independent simple random samples selected from normally distributedpopulations, and do not assume that the population standard deviations are equal. Let population 1 be females. Female BMI: n=69 x=29.14 s=7.41 Male BMI: n=79 x=28.18 s=5.24 The test statistic is The P-value is Construct a confidence interval appropriate for testing the claim in part (a). The ___% confidence interval estimate is ___<μ1−μ2<___.
The annual rainfall in a certain region is modeled using the normal distribution shown below. The mean of the distribution is 36.5 cm and the standard deviation is 5.2 cm. In the figure, V is a number along the axis and is under the highest part of the curve. And, U and W are numbers along the axis that are each the same distance away from V. Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of U, V, and W. Percentage of total area shaded: (Choose one) ▼ 200 35 | 55 25 30 40 45 50 ( cm) Submit Continue |Privacy Center © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use DIl S0 FB F7 esc F3
The following table shows the hours studied and corresponding test grade earned by students on a recent test. Calculate the correlation coefficient, r, and determine whether r is statistically significant at the 0.01 level of significance. Round your answer to the nearest thousandth. Critical Values of the Pearson Correlation Coefficient Hours Studied and Test Grades Hours Studied 0 0.5 2 2.25 3.25 3.5 3.75 3.75 4 5 1 1 81 Test Grade 72 64 68 79 85 82 72 99 87 84 97
Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.t Over a period of months, an adult male patient has taken nine blood tests for uric acid. The mean concentration was x = 5.41 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with o = 1.75 mg/dl. (a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. 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.) normal distribution of uric acid On is large O o is unknown O uniform distribution of uric acid O o is known (c) Interpret your results in the context of this problem. The probability that this interval contains the true average uric acid level for this patient is 0.95. The probability that this…
b) Find the mean and standard deviation of the difference. c) Find the rejection region and state your decision at α = 0.01.
Q2: Let X and Y have a bivariate normal distribution with parameters 4, = Hz = 1, af = 16, a 25 and p = %3D 3. The value of P(-3 < X < 3|Y = -4) is A. 0.9162 B. 0.6915 O B C. 0.6077 C
Let the X-values represent the times, in minutes, of preparation for a Statistics test; let the Y-values represent the points earned on the test. Assume that the sample of paired (X, Y) data is a simple random sample of quantitative data and the data have a bivariate normal distribution. Also, the scatterplot shows that the points approximate a straight-line pattern. If the sample has 35 pairs of values with (Zx,Zy,) = 11.41, and if we use a significance level of 0.05, calculate r and determine whether if there is sufficient evidence to support a claim of a linear correlation between X and Y.

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m-1 j=) t is the distribution of Y,? State all the relevant parameters of the evel a test (that is, the rejection region) for testing H₁ : µ; = o when of is unknown and n; is small. ntext of the test in part (b), state the Type I error and give a or the level of significance, a.