4.2.9. Let X₁, X2,..., X9 be a random sample of size 9 from a distribution that isN(μ, 0²).(a) Ifo is known, find the length of a 95% confidence interval foris based on the random variable √9(X -μ)/o.flif this interval(b) Ifo is unknown, find the expected value of the length of a 95% confidenceif this interval is based on the random variable √9(x-μ)/S.Hint: Write E(S) = (o/√n - 1)E[((n − 1)S²/0²)¹/2].interval forfl(c) Compare these two answers.

Given: Let X1, X2,.....X9 be a random sample of size 9 from a distribution that is Normal with mean…

Answered: 4.2.9. Let X₁, X2,..., X9 be a random…

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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7
A population is distributed with a known standard deviation, σ = 18 units. A random sample of size 35 is obtained from this population. The mean of this sample is 70. True or False: Since the sample size is greater than 25 the distribution of sample means from this population should be approximately normally distributed. What is the lower limit of the 95% confidence interval for the population mean μ? (2 dp) What is the upper limit of the 95% confidence interval for the population mean μ? (2 dp). Based on your confidence interval, would you believe that the true mean of this population could be 75?
6). A random sample of 90 observations produced a mean of x¯=21 from a population with a normal distribution and a standard deviation σ=4.1.
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 115, and the sample standard deviation, s, is found to be 10. (a) Construct an 80% confidence interval about μ if the sample size, n, is 25. (b) Construct an 80% confidence interval about μ if the sample size, n, is 12. (c) Construct a 70% confidence interval about μ if the sample size, n, is 25. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 108, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about μ if the sample size, n, is 16. (b) Construct a 98% confidence interval about µ if the sample size, n, is 12. (c) Construct a 70% confidence interval about u if the sample size, n, is 16. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution. (a) Construct a 98% confidence interval about μ if the sample size, n, is 16. Lower bound:; Upper bound: (Use ascending order. Round to one decimal place as needed.)
Suppose a simple random sample of size n=10 is obtained from a population with μ=68 and σ=19. Answer a-c (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution x. (b) Assuming the normal model can be used, determine P(x<71.1). (c) Assuming the normal model can be used, determine P(x≥69.2).
Assume that you have a sample of n₁ = 8, with the sample mean X₁ = 42, and a sample standard deviation of S₁ = 7, and you have an independent sample of n₂ = 13 from another population with a sample mean of X₂ = 33, and the sample standard deviation S₂ = 8. Construct a 99% confidence interval estimate of the population mean difference between μ₁ and μ₂. Assume that the two population variances are equal. ≤11-1₂5 (Round to two decimal places as needed.) (...
Let X equal the length of life of a 60-watt light bulb marketed by a certain manufacturer. We do not know the distribution of X except that Var(X) = 1158. Let u be the mean of X. Suppose a random sample of n = 25 bulbs is tested until they burn out, yielding a sample mean of = 1368 hours. (i) Compute an approximate 95% confidence interval for u. (ii) Compute an approximate 95% one-sided confidence interval for that provides a lower bound for u, i.e. compute & such that ɛ P(X - ≤ μµ)≈ 0.95.
A random sample of 28 items is drawn from a population whose standard deviation is unknown. The sample mean is = 790 and the sample standard deviation is s= 15. Use Appendix D to find the values of Student's t (a) Construct an interval estimate of u with 99% confidence. (Round your answers to 3 decimal places.) The 99% confidence interval is from to (b) Construct an interval estimate of u with 99% confidence, assuming that s= 30. (Round your answers to 3 decimal places.) The 99% confidence interval is from to (c) Construct an interval estimate of p with 99% confidence, assuming that s= 60. (Round your answers to 3 decimal places.) The 99% confidence interval is from to (d) Describe how the confidence interval changes as s increases. O The interval stays the same as s increases. O The interval gets wider as s increases. O The interval gets narrower as s increases.

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