9. For the population of infants subjected to fetal surgery for congenital anomalies the distri- bution of gestational ages at birth is approximately normal with mean u and standard de- viation o. A random sample of 15 such infants has a mean gestational age i = 30.2 weeks and a standard deviation s = 3.2 weeks. %3! %3D (a) Construct a 95% confidence interval for the true population mean u. (b) What is the length of this interval? (c) How large a sample would be required for the 95% confidence interval to have length 3 weeks? Assume that the population standard deviation o is known and thato = 3.6 weeks. (d) How large a sample would be needed for the 95% confidence interval to have length 2 weeks?
9. For the population of infants subjected to fetal surgery for congenital anomalies the distri- bution of gestational ages at birth is approximately normal with mean u and standard de- viation o. A random sample of 15 such infants has a mean gestational age i = 30.2 weeks and a standard deviation s = 3.2 weeks. %3! %3D (a) Construct a 95% confidence interval for the true population mean u. (b) What is the length of this interval? (c) How large a sample would be required for the 95% confidence interval to have length 3 weeks? Assume that the population standard deviation o is known and thato = 3.6 weeks. (d) How large a sample would be needed for the 95% confidence interval to have length 2 weeks?
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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Transcribed Image Text:9. For the population of infants subjected to fetal surgery for congenital anomalies, the distribution of gestational ages at birth is approximately normal with mean \( \mu \) and standard deviation \( \sigma \). A random sample of 15 such infants has a mean gestational age \( \bar{x} = 30.2 \) weeks and a standard deviation \( s = 3.2 \) weeks.
(a) Construct a 95% confidence interval for the true population mean \( \mu \).
(b) What is the length of this interval?
(c) How large a sample would be required for the 95% confidence interval to have length 3 weeks? Assume that the population standard deviation \( \sigma \) is known and that \( \sigma = 3.6 \) weeks.
(d) How large a sample would be needed for the 95% confidence interval to have length 2 weeks?
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