Exercise 20. Let X₁,..., Xn~ N(μ, o2) be independent, where and o are unknown. In lectureswe only discussed symmetric confidence intervals. Following the arguments we used in lectures,find an unbounded interval of the form [u, ∞) so that the mean u in satisfies P( [u, x)) = 95%.

To find an unbounded interval of the form [u, ∞) that contains the true mean u with 95% probability,…

Answered: Exercise 20. Let X₁,..., Xn~ N(μ, o2)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Use what you know about order statistics to show that for the random sample of size n = 3 the median is an unbiased estimator of the parameter θ of a uniform population with α = θ − 1/2 and β = θ + 1/2.
In random, independent samples of 400 adults and 275 teenagers who watched a certain television show, 224 adults and 121 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 95% confidence interval for p,-P2. Then find the lower limit and upper limit of the 95% 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:
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x= 6.4, y = 6.0, r= - 0.267, P-value = 0.061, and y= 7.90- 0.296x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x= 4. Use a 0.01 significance level. The best predicted value of y when x= 4 is. (Round to one decimal place as needed.)
Derive that the lower bound of one-sided confidence interval is L = Ô – CaSE[j].
In random, independent samples of 225 adults and 200 teenagers who watched a certain television show, 112 adults and 138 teens indicated that they liked the show. Let p1 be the proportion of all adults watching the show who liked it, and let p2 be the proportion of all teens watching the show who liked it. Find a 95% confidence interval for −p1p2. Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. a.) The Lower Limit is: b.) The Upper Limit is:
4. Let X₁,..., Xn N(μ,2). In this question, we will construct confidence interval for ². Let C~ x²(r), and as usual for any a € [0, 1] we denote x²(r) to be P(C>x²(r)) = a. (a) Suppose that μ is known. By considering the distribution of prove that i.i.d. prove that Xi Σ(^-^)". n i=1 [Σï_₁(Xi −µ²)² Σï-₁ (Xi − µ)²] X²/2(n) Xỉa/z(n) is a 100(1-a) % confidence interval for o². (b) Suppose that is unknown. By considering the distribution of 2 Σ(**) (X-X) (-1).5² = [Σ,(Χ. – X) Σ(Χ. – X)2] X²/2(n-1) ¹X₁-a/2 (n − 1) is a 100(1-a) % confidence interval for o². (c) In the same setting as part (b), that is, suppose that is unknown. Construct a 100(1-a)% confidence interval for o.
Let X1, . . . , Xn ∼ iid N(0, τ ). Find a pivot V (X, τ ) based on a complete sufficient statistic, andusing V (X, τ ) construct a 100γ% confidence interval for τ .
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

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS

Exercise 20. Let X₁,..., Xn~ N(μ, o2) be independent, where u and o are unknown. In lectures we only discussed symmetric confidence intervals. Following the arguments we used in lectures, find an unbounded interval of the form [u, ∞) so that the mean μ in satisfies P(μ € [u, ∞)) = 95%.