3. Let X1,... , Xn follow a Poisson distribution with rate parameter A. It is known thatthe sample mean is a consistent estimator for A. Using the central limit theorem orotherwise, show that an approximate 95% confidence interval for A can be calculatedusing the sample mean statistic, ī, as follows:x – 1.96.n* + 1.96.nGive a reason why this is an approximate confidence interval rather than an exact interval.

Answered: Image /qna-images/answer/1e862308-8f70-4a95-8c34-ed90070e9618.jpg

Answered: 3. Let X1,... , Xn follow a Poisson…

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 simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 19.4, and the sample standard deviation, s, is found to be 4.3. (a) Construct a 95% confidence interval about μ if the sample size, n, is 31. (b) Construct a 95% confidence interval about μ if the sample size, n, is 63. How does increasing the sample size affect the margin of error, E? (c) Construct a 98% confidence interval about μ if the sample size, n, is 31.How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample size is 21, what conditions must be satisfied to compute the confidence interval?
is being approxin Let X1,..., Xn be an iid with mean, µ = E(X), and variance, o2 = Var(X). True or False, and briefly explain: The sample average, X, can be expected to be closer and closer to µ as n gets bigger and pigger. Confidence Intervals
Q1. Using 625 trading days of data, you estimated the daily log return follows a normal distribution with a mean of 5 bps and and a stdev of 125 bps. Q1b. what is the 90, 95, and 99% confidence interval for your mean return estimate?
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 19.6, and the sample standard deviation, s, is found to be 5.6. (a) Construct a 98% confidence interval about u if the sample size, n, is 32. (b) Construct a 98% confidence interval about µ if the sample size, n, is 58. How does increasing the sample size affect the margin of error, E? (c) Construct a 99% confidence interval about u if the sample size, n, is 32. How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample size is 21, what conditions must be satisfied to compute the confidence interval? (a) Construct a 98% confidence interval about µ if the sample size, n, is 32. Lower bound:; Upper bound: (Round to two decimal places as needed.) C...
4. A 95% confidence inter val for a population mean µ, based on a sample of size 49, is (12.5, 20.1). (a) The sample mean, , is (i) 3.8. (ii) 16.3. (iii) 7.6. (iv) 32.6. (v) 1.96. (b) The maximum error for this confidence interval, E, is (i) 3.8. (ii) 16.3. (iii) 7.6. (iv) 32.6. (v) 1.96. (c) Compared to the 95% confidence interval, (12.5, 20.1), a 90% confidence interval based on the same sample will be (i) wider. (ii) narrower. (iii) of the same width.
Please answer this question for me because i do not understand how to work it.
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, ×, is found to be 110, and the sample standard deviation, s, is found to be 8. (a) Construct a 99% confidence interval about u if the sample size, n, is 24. (b) Construct a 99% confidence interval about u if the sample size, n, is 13. (c) Construct a 96% confidence interval about u if the sample size, n, is 24. (d) Should the confidence intervals in parts (a)(c) have been computed if the population had not been normally distributed? An example was provided with additional pictures.
Suppose that the lengths, in inches, of adult corn snakes are normally distributed with an unknown mean and standard deviation. A random sample of 38 snakes is taken and gives a sample mean of 53 inches and a sample standard deviation of 6 inches. Find a 95% confidence interval estimate for the population mean using the Student's t-distribution. Select the correct answer below: (51.36,54.64), with ME=(1.686)(638√) (51.03,54.97), with ME=(2.024)(638√) (51.00,55.00), with ME=(2.026)(637√) (51.03,54.97), with ME=(2.026)(638√) (51.34,54.66), with ME=(1.686)(637√) (51.34,54.66), with ME=(1.687)(637√)
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 104, and the sample standard deviation, s, is found to be 8. (a) Construct a 95% confidence interval about u if the sample size, n, is 22. (b) Construct a 95% confidence interval about u if the sample size, n, is 16. (c) Construct a 90% confidence interval about u if the sample size, n, is 22. (d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed? (a) Construct a 95% confidence interval about u if the sample size, n, is 22. Lower bound: 100.5; Upper bound: 107.5 (Round to one decimal place as needed.) (b) Construct a 95% confidence interval about u if the sample size, n, is 16. Lower bound: Upper bound: (Round to one decimal place as needed.)
(c) Construct a 99% confidence interval about μ if the sample size, n, is 35. Lower bound: Upper bound:
A large airline company called Fusion Fly monitors customer satisfaction by asking customers to rate their experience as a 1, 2, 3, 4, or 5, where a rating of 1 means "very poor" and 5 means "very good". The customers' ratings have a population mean of μ = 4.29, with a population standard deviation of a = 1.15. Suppose that we will take a random sample of n=7 customers' ratings. Let x represent the sample mean of the 7 customers' ratings. Consider the sampling distribution of the sample mean x. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find μ- (the mean of the sampling distribution of the sample mean). H₂=0 X (b) Find o- (the standard deviation of the sampling distribution of the sample mean). 0--0 X

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