For the population of infants subjected to fetal surgery for congenital anomalies, the distribution of gestational ages at birth is approximately normal with unknown mean µ and standard deviation sigma. A random sample of 14 such infants has mean gestational age x-bar = 29.6 weeks and a standard deviation s = 3.6 weeks. . (note: sigma is unknown, therefore t distribution)
Construct a 95% CI for the true population mean µ.
What is the length of this interval
How large a sample would be required for the 95% CI to have length 3 weeks? Assume that the population standard deviation sigma is known and that sigma = 3.6 weeks.
How large a sample would be needed for the 95% CI to have length 2 weeks?