Suppose the scores of a new standardized math test are Normally distributed with an unknown mean and an unknown standard deviation. A simple random sample of
n=25
students yields an average score of
\bar{x} =525
and a standard deviation of
s=60
. (a) Construct and interpret a
90%
confidence interval for the population mean. (b) Construct and interpret a
95%
confidence interval for the population mean. (c) What sample size would be needed to make the margin of error for the
90%
confidence no more than 7 . (d) What sample size would be needed to make the margin of error for the
95%
confidence no more than 7 .