Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter B.2, Problem 6AYU
To determine
To find: The critical values
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A sample of n = 25 scores is selected from a population with μ = 70 and σ = 20. It is very unlikely that the sample mean will be greater than 72.
True or False
For a value of population parameter 0 equal to 2, which one of the following cases corresponds
to an unbiased estimator with higher precision?
E(Ô ) = 2 and Var(Ô) = 2
E(ô – 0) = 0 and Var( ô ) = 2
E(ô – 0 ) = 2 and Var(ô ) = 1
E(Ô) = 2 and Var( Ô ) = 1
||
1.Consider the following two simple regression models :
Model I : Y, = B, + B,X, + µ;
: Y, = a, +a, (X, - )+v,
Model II
(1)
What is the estimator for B1? What is the estimator for a1?
Are they the same to each other?
Do they have the same variance?
(2)
What is the estimator for B2? What is the estimator for a2?
Are they the same to each other?
Do they have the same variance?
Chapter B.2 Solutions
Fundamentals of Statistics (5th Edition)
Ch. B.2 - True or False: The chi-square distribution is...Ch. B.2 - Prob. 2AYUCh. B.2 - Prob. 3AYUCh. B.2 - Prob. 4AYUCh. B.2 - Prob. 5AYUCh. B.2 - Prob. 6AYUCh. B.2 - In Problems 58, find the critical values 1/22 and...Ch. B.2 - Prob. 8AYUCh. B.2 - Prob. 9AYUCh. B.2 - A simple random sample of size n is drawn from a...
Ch. B.2 - NW 11. pH of Rain The following data represent the...Ch. B.2 - Travel Taxes Travelers pay taxes for flying, car...Ch. B.2 - Crash Test Results The following data represent...Ch. B.2 - Crawling Babies The following data represent the...Ch. B.2 - Peanuts A jar of peanuts is supposed to have 16...Ch. B.2 - Investment Risk Investors not only desire a high...Ch. B.2 - Critical Values Sir R. A. Fisher, a famous...
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- You are conducting a left-tailed test of a claim about a population mean when sigma is unknown with a sample size of 37.If α=.05α=.05, find the critical value, to two decimal places.arrow_forwardSuppose that a sample of T=36 recent college graduates is used estimate the model y, = B+e, where y, is the hourly wage rate. We have: y = $22.2,o² = 36 (a) Test whether the mean wage for recent college graduates is $20/hour at a = 1% (Be sure to state the null and the alternative hypotheses, the test statistics, their distribution and d.f., and your decision for this test). (b) Construct a 90% confidence interval estimation for B.arrow_forward1. In a random sample of 400 observations from a population whose variance is o?=100, we calculated F= 75. Find the 95% confidence interval estimate of the population mean µ.arrow_forward
- Find the critical value of t a/2 that corresponds to a degree of confidence of 90% and a sample size of 8.arrow_forwardWhat is the critical value for a two-tailed t test when α = 0.02 and d.f. = 18?arrow_forward1. A sample of data is collected from a group of college students (X = 112, Sx = 12, N = 58). It is hypothesized that members of this group have higher test scores than the general population (u = 100, o = 15). What test do you conduct? Don't do the test, just name the test and list the relevant equation for the test statistic. %3Darrow_forward
- Find the critical value F0 for a one-tailed test using α = 0.01, d.f.N = 3, and d.f.D = 20.arrow_forwardIF n < 30 AND T = Ý−µ -H, √n SHOW HOW THE 100(1-2x)% CONFIDENCE INTERVAL FOR U IS DERIVEDarrow_forwardIf the sample data are in the critical region with α = 0.01 and Ho is rejected, then one could still reject Ho even if α were changed to 0.05. Is this statement True or False?arrow_forward
- Question 2. and variance o² = 4. (a) (b) Assume a random loss X follows a normal distribution with mean =1 Calculate the Value at Risk of X at the 95% level, i.e., VaRo.05(X). For a given constant c E IR, show that VaR,(X + c) = VaRp(X) +c for p E (0, 1).arrow_forward1. In a trivariate distribution: 01 = 3, 02 = 4, 03 = 5 123 = 0.4, 131 = 0-6, 13 = 0-7 Determine the regression equation of X1 on X2 and X3 if the variates are measured from their means.arrow_forwardA random sample of n = 9 scores is obtained from a population with µ = 50 and σ = 9. If the sample mean is M = 53, what is the z-score corresponding to the sample mean?arrow_forward
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