Let Y, represent the ith normal population with unknown mean 4, and unknown varianceof for i=1,2. Consider independent random samples, Ya, Y2Yin, of size n,, fromthe ith population with sample mean Y, and sample variance S? =(Y-P.².(e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument.(f) Find a (1-a) x 100% confidence interval for of(g) For non-zero constants a,'s, what is the distribution of U₂ = a₁Y₁-0₂Y₂? State allthe relevant parameters of the distribution.

Answered: Let Y, represent the ith normal…

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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Conduct a realted-sample t-test using the following data set. Each row represents a pairof scores A B 18 4 35 40 31 14 30 18 40 30 25 27 11 17 30 18 28 12 20 20 determine critical values (for an alpha of .05) that you should use to evaluate this t-score and compute r^2 for this test.
3. Assume that the distribution of the length X of male spider is N(ux,o}) and the length Y of female spiders is N(µy,o?), and X and Y are independent. Construct approximated 95% one-sided confidence intervals for o? /o? when n = m = 30, and = 0.4399 and S? = 1.4100.
Suppose you fit a simple Poisson model such that in A = XB where B = 1.9. What would the variance be if x = -0.8 ?
4.2 A sample of 19 female bears was measured for chest girth (y) and neck girth (x), both in inches. The least squares regression equation relating the two variables is = 5.32 + 1.53 x. The standard deviation of the regression is s = 3.692. y^ 4.2.1 What is a 95% confidence interval for the average (or mean) chest girth for bears with a neck girth of 20 inches? The standard error of the fit is s.e.(fit) = 0.880 a. (27.9, 43.9) b. (28.1, 43.7) c. (34.1, 37.8) d. None of the above 4.2.2 Interpret the confidence interval obtained in 4.2.1
Suppose X1,..., Xn is a random sample from an exponential distribution with mean e. If X = 17.9 with n = 50, find (a) a one-sided 95% confidence interval for 0, and (b) a two-sided 95% confidence interval for 0.
The Wilcoxon signed-rank test can be used to perform a hypothesis test for a population median, η, as well as for a population mean, µ. Why is that so?
2. We performed a linear regression using 25 observations. From the regression output we find that bo = 5.7, bị = 12.9, x = 11.4, Sz = 3.2 and MSE = 12.25. a. From the least squares line, what is the predicted response when x* = 10.65? y = b. What is the 95% confidence interval for the mean response when x* = 10.65? c. What is the 95% prediction interval for an individual response when x* = 10.65? d. Which interval is wider? The confidence interval or the prediction interval? O a. Confidence Interval b. Prediction Interval
Pls solve it quickly..
Construct a 99% confidence interval for u, - H, with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances Stats X, = 98 mg, s,= 3.81 mg, n, = 14 x = 65 mg, s, =222 mg, n, =20 Confidence interval when variances are not equal +t. n2 d.f. is the smaller of n, - 1 or n, - 1 Enter the endpoints of the interval
A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 H2 O Ho: H1 = l2; H1: H1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's…
IID Suppose X1, ..., X, N(u, o?). Construct a 95% confidence interval for o? when u is known.
The expectation of X, which is also known as the mean or average, is E(X) = 7 and the Variance of X is var(X) =4. Using the equation Y = 11X + 81. What are the expected value E(Y), variance VAR(Y), and standard deviation SD(Y) of this expression.

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