10. A simple random sample of size n is drawn from apopulation that is known to be normally distributed. Thesample variance, s², is determined to be 19.8.(a) Construct a 95% confidence interval for o² if the samplesize, n, is 10.(b) Construct a 95% confidence interval for o² if the samplesize, n, is 25. How does increasing the sample size affect thewidth of the interval?(c) Construct a 99% confidence interval for o² if the samplesize, n, is 10. Compare the results with those obtained inpart (a). How does increasing the level of confidence affectthe width of the confidence interval?

Answered: 10. A simple random sample of size n is…

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 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?
27. Bob selects independent random samples from two populations and obtains the values î1 0.700 and p2 = 0.500. He constructs the 95% confidence interval for p1 – P2 and gets: 0.200 + 1.96(0.048) = 0.200 ± 0.094. Note that 0.048 is called the estimated standard error of pi – p2 (the ESE of the estimate). Tom wants to estimate the mean of the success rates: Pi +P2 2 (a) Calculate Tom's point estimate. (b) Given that the estimated standard er- ror of (p1 + P2)/2 is 0.024, calculate the 95% confidence interval estimate of (Pi + P2)/2. Hint: The answer has our usual form: Pt. est. +1.96 × ESE of the estimate.
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