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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Construct a 90% confidence interval for u, - , with the sample statistics for mean calorie content of two bakeries specialty pies and confidence interval construction formula below Assume the populations are approximately normal with equal variances Bakery A Bakery B X1 = 1823 cal X, = 1629 cal S1 = 155 cal S2 = 190 cal n1 = 10 n2 = 12 Confidence interval when variances are equal n n. (n. - 1) s (n2 - 1) s where G and d.f = n, +n2 - 2 nn, - 2 Enter the endpoints of the interval (Round to the nearest integer as needed.)
Answer last 3 parts. t hank y o u.
18. Two random variables have the regression equations : 3 X+2Y - 26 = 0 6X+ Y- 31 = 0 Find the mean value and the coefficient of correlation between X and Y. If the variable of X 25, find the standard deviation of Y from the data given above. tem (be scue)
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.
Deal with it.I need the correct answer
11. Consider a random sample Y₁, Y2, ..., Yn from a normal population Y~N(μ, o²) where the population variance and mean are unknown. We want to construct a Σ(X-X)² Show 100(1 a)% confidence interval for the population variance if g² whether or not is a pivotal quantity and construct a 100(1-a) confidence interval.
Suppose that X₁,..., Xn are i.i.d. from a normal population with mean μ and variance o². Calculate the expected value and the variance of the sample mean X and find the distribution of √n(X − µ).
Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let Width (C.I) = the width of the confidence interval for the average value y for a given value of x, and Width (P.I) = the width of the prediction interval for a single value y for a given value of x. Which of the following statements is true? Width (C.I) = 0.5 Width (P.I) Width (C.I) = Width (P.I) Width (C.I) > Width (P.I) Width (C.I) < Width (P.I)
X. is found to be 19.1, and the A simple random sample of sizen is drawn from a population that is normally distributed. The sample mean, sample standard deviation, s, is found to be 4.9. (a) Construct a 96% confidence interval about u if the sample size, n, is 39. (b) Construct a 96% confidence interval about u if the sample size, n, is 68. How does increasing the sample size affect the margin of error, E? (c) Construct a 98% confidence interval about u if the sample size, n, is 39. How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample size is 14, what conditions must be satisfied to compute the confidence interval? (a) Construct a 96% confidence interval about u if the sample size, n, is 39. Lower bound: Upper bound: (Round to two decimal places as needed.) (b) Construct a 96% confidence interval about u if the sample size, n, is 68. Lower bound: ; Upper bound: (Round to two decimal places as needed.) How does increasing the sample…
You wish to conduct a hypothesis test to determine if a bivariate data set has a significant correlation among the two variables. That is, you wish to test the claim that there is a correlation (Ha : p ‡ 0). You have a data set with 7 subjects, in which two variables were collected for each subject. You will conduct the test at a significance level of a = 0.05. Find the critical value for this test. rc.v. = ± Report answers accurate to three decimal places.
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
The following data represent the length of time, in days, to recovery for patients randomly treated with one of two medications to ciear up severe bladder infections. Find a 95% confidence interval for the difference u,-H, between in the mean recovery times for the two medications, assuming normal populations with equal variances. Medication 1 x, 13 s = 14 s =1.6 n, = 14 Medication 2 n211 X2= 16 Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table ofcritical values of the t-distribution The confidence interval is

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