b) Let X₁, X₂,..., X and Y₁, Y₂, ..., Ym be random samples from populations with moment generating25functions Mx₁(t) = ³t+t² and My(t) = (₁-¹)²5, respectively.i) Find the samplingdistribution of the statistic W = X₁ + 2X₂ − X3 + X4 + X5.ii) What is the value of the sample size n, if P[Σ1(X¡ − X)² > 68.3392] = 0.025?iii) What is the value of the sample size m, if P(|Ỹ - µy| ≥10) < 0.04?

Answered: Image /qna-images/answer/e9543bc7-8d60-4efa-a7ce-e07255ebfd56.jpg

Answered: i) Find the sampling distribution of…

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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A one-sample zz-test for a population proportion pp will be conducted. Which of the following conditions checks that the sampling distribution of the sample proportion is approximately normal? 1. The sample is selected at random. 2. np0≥10np0≥10 and n(1−p0)≥10n(1−p0)≥10 for sample size nn. 3. The sample size is less than or equal to 10 percent of the population size. a. 1 only b. 2 only c. 3 only d. 1 and 2 only e. 1,2, and 3 only
Suppose a simple random sample of size n=125 is obtained from a population whose size is N=10,000 and whose population proportion with a specified characteristic is p= 0.4
Suppose a simple random sample of sizen3200 is obtained from a population whose size is N=20,000 and whose population proportion with a specified characteristic is p= 0.4. Complete parts (a) through (c) below. ... (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. OA Not normal becausens0.05N and np(1-p) 10. OC. Not normal becausens0.05N and np(1-p) 10. O D. Approximately normal because n<0.05N and np(1-p) < 10. Determine the mean of the sampling distribution of p. HA= 0.4 (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. on = 0.034641 (Round to six decimal places as needed.) (b) What is the probability of obtaining x = 90 or more individuals with the characteristic? That is, what is P(p20.45)? P(p20.45) = (Round to four decimal places as needed.) Clear all Check answer
3. Let Y₁ 5)
Suppose a simple random sample of size n equals 1000 is obtained from a population whose size is N equals 2 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.75. Complete parts (a) through (c) below.
Please answer parts B,C and D
state whether or not this resulting observed interval ended up capturing the true population proportion p of 0.45.

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i) Find the sampling distribution of the statistic W = X₁ + 2X2 − X3 + X4 + X5. ii) What is the value of the sample size n, if P[Σ²²=₁(X¡ – X)² > 68.3392] = 0.025? - - iii) What is the value of the sample size m, if P(|Ỹ – µỹ| ≥10) <0.04?