Given are five observations for two variables, x and y. (Round your answers to two decimal places.)X, 1 2Y₁3 7 5 10 14(a) Use Sp.= SV3 4 5(x*- x)²+n Σ(Χ. – x)2(c) Use Spred S√ 1 +(b) Use p* ±ta/25p. to develop a 95% confidence interval for the expected value of y when x = 4.to(d) Use 9 ±ta/25 predtonto estimate the standard deviation of * when x = 4.+(x*- x)²Σ(x, - x)²to estimate the standard deviation of an individual value of y when x 4.to develop a 95% prediction interval for y when x = 4.

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Answered: Given are five observations for two…

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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For a 98% confidence interval of the population mean based on a sample of n = 20 with s = 0.05, the critical value of t is:
The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with ? = 0.32 and that x = 5.21. (Use ? = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5?State the appropriate null and alternative hypotheses. H0: ? = 5.5Ha: ? ≠ 5.5H0: ? = 5.5Ha: ? ≥ 5.5 H0: ? = 5.5Ha: ? < 5.5H0: ? = 5.5Ha: ? > 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is sufficient evidence…
Suppose X1, . . . , Xn be a random sample from the Beta(θ, 1) distribution. Find the P-value for the LRT test of the hypotheses H0 : θ ≥ 1 vs H1 : θ < 1
b) Find the critical value of t for a 90% confidence interval with df=58.
In a hypothesis test with hypotheses Ho: μ ≤ 54 and H1: μ > 54, a random sample of 24 elements selected from the population produced a mean of 58.6 and a standard deviation of 13.4. The test is to be made at the 10% significance level. Assume the population is normally distributed. What is the critical value of t ?
A researcher obtains t=2.25 for a repeated measures study using a sample of n=10 participants. Based on this t value, what is the correct decision for a two- tail test at .05 and .01 alpha level?
Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown. Consider the 3 estimators T1 = X + Y − Z, T2 = 2X + Y + Z 4 , T3 = 3X + Y + Z 5 . (a) Which among the above estimators are unbiased? (b) Among the class of unbiased estimators, which has the minimum variance?
For a random sample of 50 measurements of X1, sample mean x ̄1 = 200, sample standard deviation s1 = 10. For X2, from a random sample of 50, sample mean x ̄2 = 190 and sample standard deviation s2 = 15. Assume that population distributions are approximately independent normal with unequal variances. Answer the following questions 1 through 3. 1. Construct a 90% confidence interval for μ1 − μ2. (i) State the assump- tions, (ii) show your work, and (iii) interpret the result in context of the problem. 2. Using the same samples, you want to test whether the difference between two population means is 5 or not at the significance level α = 0.1. H0 : μ1 − μ2 = 5 vs H1 : μ1 − μ2 ̸= 5. What would your conclusion be? Support your answer briefly. You don’t need to conduct the hypothesis test.
To test H0: σ=4.5 versus H1: σ≠4.5, a random sample of size n=14 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s=6.7, compute the test statistic. (b) If the researcher decides to test this hypothesis at the α=0.10 level of significance, determine the P-value. (c) Will the researcher reject the null hypothesis?
If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameter
In Exercise 4.2.27, in finding a confidence interval for the ratio of thevariances of two normal distributions, we used a statistic S21/S22, which has an Fdistributionwhen those two variances are equal. If we denote that statistic by F,we can test H0 : σ21 = σ22 against H1 : σ21 > σ22 using the critical region F ≥ c. Ifn = 13, m = 11, and α = 0.05, find c.
Let X1, · · · , Xn be drawn independently from a distribution with density 1. f(x|θ) = 2/β, θ − 0.25β < x < θ + 0.25β, where β is a positive constant. 2. f(x|θ) = 2x/θ 2 , 0 < x < θ, θ > 0. 3. f(x|θ) = e θ−x for x > θ. For each of the above three cases, construct a 95% confidence interval for θ.

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