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
1. Assume there are a population size N = 6 with units (2,4,6,8, 10, 12), and out of which sample size n = 5 units are to be selected based on simple random sampling without replacement. a. Prove that the mean of the sample is unbiased estimator for the population mean. b. Find the mean and variance of the random variable Y = (*/) + 10, where si = (x;-1)² is unbiased estimator of the variance of the random sample X 22-1 to the population variance, and X is the population mean. 2. Prove that the simple random sampling without replacement is more efficient than simple random sampling with replacement.
3. Let Y₁ 5)
A random sample of size 18is to be taken from a population that is normally distributed with mean 45 and standard deviation 10. The sample mean of the observations in our sample is to be computed. The sampling distribution of the sample mean is.....
A population of values is normally distributed with μ = 84.5 and σ = 85.3. a) Find P72 for a single randomly selected value. This answer represents the score separating the bottom 72% scores from the top 28% scores. P72 = b) Now draw a random sample of size n = 96. Find P72 for the sampling distribution. This answer represents the score separating the bottom 72% of the sample means from the top 28% of the sample means. P72 = Enter your answers as numbers accurate to 1 decimal place.
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.
2.Given a random sample of size n = 29, from a normal distribution, find k such that: a) P(-k < T < 1.313) = 0.88 b) P(-k < T < k) = 0.99 c) P(-2.286 < T < k) = 0.685
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.
a) Let X₁, X2, X3,..., X₁ be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter 0 and Y = ===1 X₁. n b) i) Show that y follows a chi-square distribution with 2n degrees of freedom. ii) What is the value of the sample size n, if P(Y > 20.4831) = 0.025? iii) What is the value of sample size n, if P(|Y - 2n| <40) ≥ 0.025? iv) Use the Central Limit Theorem to compute P(100 < Y < 115), for n = 40. Let X₁, X2, ..., X5 be a random sample of size 5 from the standard normally population. If the statistic Y is given by Y = X1 X2 X3 ₁²+X3² +X5² i) Briefly explain why Y follows a Student's t distribution with 3 degrees of freedom. ii) Compute the probability that Y is between 2.35 and 5.84. iii) What is the mean and variance of the statistic Y?

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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?