A) Consider a population with known variance σ2 = 4. In a simple random sample of sizen = 15 we find ¯x = 3.
(a) Construct a 95% confidence interval for the population mean µ.
(b) Construct a 90% confidence interval for the population mean µ.
(c) Construct a 99% confidence interval for the population mean µ.
(d) Would an 85% confidence interval be wider or narrower than the 90% confidence interval? Answer this question without doing any calculations.
B) We take a simple random sample of size 50 from a population with unknown variance. We find the sample mean is ¯x = 25 and the sample standard deviation is s = 15.
(a) Give the 90% confidence interval for the population mean µ.
(b) Give the 95% confidence interval for the population mean µ.
(c) Give the 99% confidence interval for the population mean µ.