Recall the simple regression modelY = a + 3X + €where the random error & ~ N(0,02). Let 3 be the MLE estimator of the slope ß. InHomework 3 Exercise 3, we found the distribution of this point estimator to beجور عليهB~N0²nVxwhere v is the variance of the empirical distribution of x1, x2,, Xn. (i) Verify thatP(|3 – ß| ≤ €) = 1 - aand conclude that, if σ is known,Xi:Yi:Xi:Yi:O/nVTis a 100(1 a)% confidence interval of B.(ii) Suppose we know that σ = 2 and are given the following data points (x₁, yi):oZa/212Give a 95% confidence interval of 3¹.E =B + Za/27OZa/21 /nvxO/nv x4.44 5.18 -3.08 3.99 4.39 3.3 -1.25 1.0314.1116.61 -0.58 15.78 13.2 12.692.93 5.274.091.514.254.33 -2.75 -2.85 -2.57 3.1615.56 -2.43 -4.66 0.59 11.6713.816.07 14.78

Given that β^~Nβ, σ2nvx, where vx is the variance of the empirical distribution of x1, x2,..., xn.…

Answered: (i) Verify that P(|38| ≤e) = 1-a and…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

You are performing a two-tailed matched-pairs test with 39 pairs of data.If α=0.2, find the positive critical value, to two decimal places.
5
If P(A) = 0.52, P(B) = 0.45 and P(A u B) = 0.76, then P(B | A) = (Enter a number between 0 and 1, using two decimal points)
From the image: The regression output was based on a sample of 213 cane toads. How many degrees of freedom does the appropriate t-distribution used to get the p value and the t∗ critical value for confidence intervals have?
Example 15.12) On the basics of the following data, determine regression of Y on X: ΣΧ231 ΣΥ- 498 ΣΧ 4903 EX = = 21582 EXY= 10211 n = 12 Also estimate the confidence interval of the regression coefficient.
For each example, choose the confidence interval that has a larger margin of error. 1) OA 90% confidence interval for a mean contructed from a sample of 55 OA 90% confidence interval for a mean contructed from a sample of 45 2) OA 90% confidence interval for a mean constructed from a sample of 45 OA 92% confidence interval for a mean constructed from a sample of 45 3) OA 90% confidence interval for a mean constructed from a sample of 45, using s OA 90% confidence interval for a mean constructed from a sample of 45, using o
[4.2.14. Let X denote the mean of a random sample of size 25 from a gamma-type distribution with a = 4 and B > 0. Use the Central Limit Theorem to find an approximate 0.954 confidence interval for u, the mean of the gamma distribution. Hint: Use the random variable (X- 43)/(432/25)/2 = 5X/23- 10. %3D
2.4 Compute the 95% confidence interval for the population (true) value of prediction computed in question 2.3, and interpret it in words as well as graphically. The formula for the 95% confidence interval around a predicted Y value is: Y= Î±zerit(a=.05, 2 tailed)*sy.x Define and give the values for the following the terms in the formula. Î: 4.15504 Zsit: 0.025 Sy-x: 1.593 The numerical values for the confidence interval are:
A 95% confidence interval for u was given as -5.65 < u < 2.61. What would a test for Ho : µ = 0 vs H1 : µ # 0 conclude? A. reject the null hypothesis at a = 0.05 and all smaller a B. fail to reject the null hypothesis at a = = 0.05 and all smaller a C. reject the null hypothesis at a = 0.05 and all larger a D. fail to reject the null hypothesis at a = - 0.05 and all larger
A movie studio wishes to determine the relationship between the revenue from the rental of comedies on DVD and videotape and the revenue generated from the theatrical release of such movies. The studio has bivariate data from a sample of 13 comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from DVD and videotape rentals (in millions of dollars) for each of the 13 movies. The least- squares regression equation computed from the data is y= 3.57+0.13x. The studio has plans for the DVD/video release of a comedy that grossed about 40.5 million dollars in theaters. The studio has predicted the rental revenue from this release using the regression equation and is now interested in both a prediction interval for this rental revenue and a confidence interval for the mean rental revenue of movies generating this same theater revenue. The studio has already computed the following for their data: • mean…
A 100(1 - α)% confidence interval for the mean μ of a normal population when the value of σ is known is given by (x-²a/2" Six+ .za/2 VM). By how much must the sample size n be increased if the width of the CI above is to be halved? Halving the length requires n to be increased by a factor of If the sample size is increased by a factor of 16, what effect will this have on the width of the interval? Increasing the sample size by a factor of 16 will ---Select-- the length by a factor of ---Select-- increase Need Help? Read It decrease
K For parts a and b, use technology to estimate the following. a) The critical value of t for a 90% confidence interval with df = 5. b) The critical value of t for a 99% confidence interval with df = 104.

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS