2. Consider X1, X2, X, iid N(4,0²) where o is known. In this problem we show that among the (1 – a) confidence intervals of the form , P1 + P2 = a, the one with the choice pi = P2 = is the shortest. This explains why the symmetric confidence interval is preferred among all possible choices (unless we want to explicitly construct a one sided confidence interval). a. Without loss of generality, suppose pi < P2. Draw a picture of the standard Normal pdf with z,ı: p2; Za/2: Use it to show that Zp2 < Za/2 < Zpı•

2. Consider X1, X2, X, iid N(4,0²) where o is known. In this problem we show that among the (1 – a) confidence intervals of the form , P1 + P2 = a, the one with the choice pi = P2 = is the shortest. This explains why the symmetric confidence interval is preferred among all possible choices (unless we want to explicitly construct a one sided confidence interval). a. Without loss of generality, suppose pi < P2. Draw a picture of the standard Normal pdf with z,ı: p2; Za/2: Use it to show that Zp2 < Za/2 < Zpı•

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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Similar questions

a) Determine 99% confidence limits for beta(symbol couldn't write) (the slope of the regression line) and alpha (the intercept of the regression line). b) 34. Determine 99% prediction limits for Y when X = 41.7 and 95% prediction limits for Y when X = 61.5. c) draw a scatter plot.
Suppose a 95% confidence interval for μ runs from 38 to 46. If we had tested H0: μ = 35 against H1:μ ≠ 35 using α = 0.05, we would a) have retained H0 b) not be able to decide about H0 unless n were given c) not be able to decide about H0 unless n and σ were given d) have rejected H0 The correct answer is d: have rejected H0. Please explain and provide a solution.
Suppose the data are independent observations sampled from some population distribution. In which of the following circumstances we would NOT be safe to construct a one-sample t confidence interval for a population mean based on a simple random sample from a huge population? (Select one answer.) (i) The sample size is 5, and we know from past experience that the population distribution is normal. (ii) The sample size is 10, and the observations are 0, 0, 0, 0, 0, 0, 0 ,1 ,1 ,18. iii) The sample size is 45 and the boxplot of the data is 2 6. 10 14 18 (iv) The sample size is 1800 and the histogram of the data is 10 20 30 40 50 (v) It's not safe to construct t confidence intervals in any of the circumstances above.
10. A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample variance, s², is determined to be 19.8. (a) Construct a 95% confidence interval for o² if the sample size, n, is 10. (b) Construct a 95% confidence interval for o² if the sample size, n, is 25. How does increasing the sample size affect the width of the interval? (c) Construct a 99% confidence interval for o² if the sample size, n, is 10. Compare the results with those obtained in part (a). How does increasing the level of confidence affect the width of the confidence interval?
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1) When we compute a 95% confidence interval (CI) using a sample meana. 95% of the time it will include the population mean b. we have an interval estimate of population meanc. 5% of the time it will not include the population mean d. we can't be absolutely sure population mean is in the CIe. all the above are correct 2) In R, what argument does the function: str( ) expect? a. name of an object b. proper punctuation c. xlim d. plot e. col=8 f. pch g. The function name h. none of the above
In random, independent samples of 200 adults and 300 teenagers who watched a certain television show, 124 adults and 153 teens indicated that they liked the show. Let p, be the proportion of all adults watching the show who liked it, and let p, be the proportion of all teens watching the show who liked it. Find a 90% confidence interval for p,-p,. Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary, consult a list of formulas.) Lower limit: Upper limit: O O
4. With a sample of n = 11 participants, the repeated-measures t statistic has df = 10, M, = -4, SMb = 0.887 at two-tailed hypothesis testing. Compute for the confidence interval with 99% confidence. Show your solution. ( - %3D
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4. A 99% confidence interval for the mean u of a population is computed from a random sample and found to be 6+ 3. We may conclude that (a) there is a 99% probability that u is between 3 and 9. (b) the true mean is 6 and the true margin of error is 3, both with 99% probability. (c) if we took many, many additional random samples, and from each computed a 99% confidence interval for µ, approximately 99% of these intervals would contain u. (d) All of the above.