a) Let X₁, X₂, X3,..., X, be a random sample of size n from population X. Suppose that X~N(0, 1)youand Y = -√n.VRi) Show that the standard score of the sample mean X, is equal to Y.ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively.iii) Show using the moment generating function technique that Y is a standard normal rando...variable.iv) What is the probability that Y² is between 0.02 and 5.02?b) Let X₁, X₂, X, and Y₁, Y₂.... Y be random samples from populations with moment generatingfunctions Mx, (t) = eat+t² and My (t) = (-), respectively.25i) Find the sampling distribution of the statistic W = X₁ + 2X₂ X3 + X₁ + X5.ii) What is the value of the sample size n, if PIX(X-X)2> 68.3392] = 0.025?iii) What is the value of the sample size m, if P(|Y-Hy ≥10) <0.04?QUESTION A

It is given that X follows N(θ, 1), then E(X) = θ and V(X) = 1, And the moment genarating function…

Answered: i) Show that the standard score of the…

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

Suppose that the lengths of human pregnancies are normally distributed with a mean of 267 days and a standard deviation of 16 days. Complete the following statements. (a) Approximately ? of pregnancies have lengths between 219 days and 315 days. (b) Approximately 95% of pregnancies have lengths between I days and days.
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shipping time, μ, spent by customers at the supermarkets has been reported to be 40 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that μ is less than 40 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 34 minutes and the standard deviation of the times to be 16 minutes. Based on the information, answer the questions below.
a) Find the F-test statistic to test the claim that the variances of the two populations are equal. Both distributions are normal. The populations are independent. The standard deviation of the first sample is 2.6282.6681 is the standard deviation of the second sample. B) Find the F-test statistic to test the claim that the population variances are equal. Both distributions are normal. The standard deviation of the first sample is 4.15966.3763 is the standard deviation of the second sample.
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, u, spent by customers at the supermarkets has been reported to be 35 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that u is greater than 35 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 42 minutes and the standard deviation of the times to be 10 minutes. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? H: u is ? H: u is ? In the context of this test, what is a Type I error? A Type I error is ? fact, u is ? ? v when, in v the hypothesis that u is? v? v. Suppose that the consultant decides to reject the null hypothesis. What sort of error might she be…
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, u, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate u. Assuming that the standard deviation of the population of shopping times at the supermarkets is 27 minutes, what is the minimum sample size she must collect in order for her to be 99% confident that her estimate is within 5 minutes of u? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) ?
The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn, without burning it, are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds. Suppose two independent random samples, 25 of each, are taken and the mean popping times are calculated. Let R = the popping time of a randomly selected regular-sized bag and M = the popping time of a mini-sized bag. Which of the following best describes the mean of the sampling distribution of ? A) –50 B) 50 C) 90 D) 140
can you please provide explanations
Assume the sample variances to be continuous measurements. Find the probability that a random sample of 31 observations, from a normal population with variance of 6, will have a sample variance between 3.33 and 9,99 Select one: Oa. 0.975 Ob. 0.011 Oc 0.985 Od. 0.965
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, µ, spent by customers at the supermarkets has been reported to be 40 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that u is greater than 40 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 44 minutes and the standard deviation of the times to be 15 minutes. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? Hiµ is ? H: p is ? In the context of this test, what is a Type II error? A Type II error is ? fact, u is ? the hypothesis that u is when, in Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making?
Assume that a high school principal believes that high number of absences hinders the students' ability to perform on standardized tests. He randomly selects a sample of 9 students who had 5 or more absences in the school year. The average ACT Composite score for this sample is X = 19 with s = 4.9. ACT Composite scores are normally distributed with u = 21.0. Do the data support the claim that the high number of absences hinders the students' ability to perform on standardized tests, using a = .05? Please show the four-step hypothesis test. %3D
The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn without burning it are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds. Suppose two independent random samples, 25 of each, are taken and the mean popping times are calculated. Let R = the popping time of a randomly selected regular-sized bag and M = the popping time of a mini-sized bag. Which of the following best describes the shape of the sampling distribution of ? Normal because both population distributions are Normal uniform because the both sample sizes are less than 30 skewed right because the difference in times cannot be negative skewed left because the sample sizes are less than 30 and the sampling variability is unknown
Find the m.g.f of uniform distribution and hence find its mean and variance.

SEE MORE QUESTIONS

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

i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal rando... variable.