Consider the hypothesis test Ho: M₁ = μ₂ against H₁ : µ₁μ₂. Suppose that sample sizes are n₁ = 15 and m₂ = 15, that x₁ = 4.9and x₂ = 7.6 and that s² = 4 and s = 6.21. Assume that o² = 0 and that the data are drawn from normal distributions. Useα = 0.05.(a) Test the hypothesis and find the P-value.(b) What is the power of the test in part (a) for a true difference in means of 3?(c) Assuming equal sample sizes, what sample size should be used to obtain ß = 0.05 if the true difference in means is - 2? Assumethat a = 0.05.(a) The null hypothesis(e.g. 98.7654).(b) The power is i(c) n₁ = n₂ =Telrejected. The P-value is i. Round your answer to four decimal places. Round your answer to two decimal places (e.g. 98.76).. Round your answer to the nearest integer.

Answered: Image /qna-images/answer/551f5737-8efc-4f9d-9428-196f7b14dcda.jpg

Answered: Consider the hypothesis test Ho: M₁ =…

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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Calculate the test-statistic, t with the following information for a Two Independent Samples t Test with Ha:μ1-μ2≠0. Be sure to first determine if you need to pool or not.n1=60, ¯x1=2.53, s1=0.53n2=50, ¯x2=2.69, s2=0.96Round to 3 decimal places. t =__________ It is pool or not?________
Assume that you have a sample of n1=8, with the sample mean X1=44, and a sample standard deviation of S1=4, and you have an independent sample of n2=6 from another population with a sample mean of X2=35 and the sample standard deviation S2=5. Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that μ1>μ2? Find the p-value. p-value=__________ (Round to three decimal places as needed.)
Let a = 0.05. (a) Suppose that we sample from a bivariate normal distribution with p = 0.5. Assuming that we observe r = 0.5, how large a sample will be needed to reject Ho: p= 0 in favor of Ho: p=0? (b) Suppose that we sample from a bivariate normal distribution with p = 0.1. Assuming that we observe r = 0.1, how large a sample will be needed to reject Ho: p= 0 in favor of Ho: p0?
Use the calculator displays to the right to make a decision to reject or fail to reject the null hypothesis at a significance level of α=0.05. Z-Test Z-Test Inpt: Data Stats μ≠80 μ0:80 z=−1.41421356 σ:3.75 p=0.15729921 x:79.25 x=79.25 n:50 n=50 μ: ≠μ0 <μ0 >μ0 Calculate Draw Question content area bottom Part 1 Choose the correct answer below. A. Since the P-value is greater than α, fail to reject the null hypothesis. B. Since the P-value is less than α, reject the null hypothesis. C. Since the P-value is greater than α, reject the null hypothesis. D. Since the P-value is less than α, fail to reject the null hypothesis.
After you estimate a simple linear regression you obtain the following sample regression function: Y₁ = 8.8 +0.7091 Xį With an r² of 0.784. The observed dependent variable used for the regression is: Y 9 675 40 40 40 6 5 5 5 5 1 1 Compute the sample variance of X? 8.45 10.79 9.17 7.19 Cannot be computed with the provided information.
For each residual plot below, decide on whether the usual assumptions: "Y₁ = Bo + B₁2; + €, i = 1,..., n, ₁ independent N(0,0²) random variables" of simple linear regression are valid or not. If some assumptions seem invalid, choose the options(s) which indicate the most obvious departures from the model assumptions. Note: For a small sample, the normality assumption cannot be "proved", but it can be "violated" if there is an extreme residual (outlier). Parta) y-axis has residual, x-axis has x-variable with values 1,2,...,10. (Click on graph to enlarge) Which is/are the best answer(s) for the residual plot (a)? A. linear relation assumption is invalid B. the normality assumption is invalid C. constant variance assumption is invalid D. assumptions seem reasonable E. None of the above
Use the calculator displays to the right to make a decision to reject or fail to reject the null hypothesis at a significance level of α=0.10. Z-Test Z-Test Inpt: Data Stats μ≠80 μ0:80 z=−1.18321596 σ:3.75 p=0.23672357 x:79.25 x=79.25 n:35 n=35 μ: ≠μ0 <μ0 >μ0 Calculate Draw Choose the correct answer below. A. Since the P-value is greaterthan α, fail to reject the null hypothesis. B. Since the P-value is lessthan α, reject the null hypothesis. C. Since the P-value is lessthan α, fail to reject the null hypothesis. D. Since the P-value is greaterthan α, reject he null hypothesis.
A population of values has a normal distribution with μ=116.3μ=116.3 and σ=27.5σ=27.5. You intend to draw a random sample of size n=249n=249.Find the probability that a single randomly selected value is greater than 117.3.P(X > 117.3) = Find the probability that a sample of size n=249n=249 is randomly selected with a mean greater than 117.3.P(¯xx¯ > 117.3) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
REQUIRED: • construct the rejection region. • Show the solution in a step-by-step procedure. • state the null and alternative hypotheses • state the null and alternative hypotheses • determine the critical value and sketch the rejection region and non-rejection region in the normal curve.
For the given data, (a) find the test statistic, (b) find the standardized test statistic, (c) decide whether the standardized test statistic is in the rejection region, and (d) decide whether you should reject or fail to reject the null hypothesis. The samples are random and independent. Claim: μ₁ μ₂, α=0.01. Sample statistics: x₁ = 1230, n₁ = 50, x₂ = 1200, and n₂ = 80. Population statistics: ₁ = 65 and ₂ = 110. C (a) The test statistic for H₁-H₂ is. (b) The standardized test statistic for H₁-H₂ is (Round to two decimal places as needed.) (c) Is the standardized test statistic in the rejection region? Yes O No (d) Should you reject or fail to reject the null hypothesis? Hoi H2Hzi Hai Hy
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with o = 69. Let u denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? O Ho: H > 1,300 H: u = 1,300 Ο H,: μ= 1,300 H: u 1,300 (b) Let X denote the sample average compressive strength for n = 15 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). What is the probability distribution of the test statistic when Ho is true? O The test statistic has a binomial distribution. O The test statistic has a gamma distribution. The test statistic has a normal distribution. O The test statistic has an exponential distribution. If X = 1,340, find the…
In a test of H0: μ = 14 against HA: μ < 14, the sample data with sample size 25 from a normal distribution yielded a test statistic Tobs = -3.15. Bracket the p-value for the test.

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