The standard deviation for the checking account balances is assumed known to be $357.50. Recently, a bank manager was interested in estimating the mean balance. To do this, she selected a random sample of 81 accounts and found a mean balance of $1,347.20. At a 95 percent confidence level, the lower limit for the confidence interval is $646.50.

Question

Quizplus · Accepted Answer

The calculation for the lower limit of a confidence interval for the mean, assuming the standard deviation is known, is given by $\bar{x} - Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-value corresponding to the confidence level (for 95%, $Z = 1.96$), $\sigma$ is the population standard deviation, and $n$ is the sample size. Given $\bar{x} = 1347.20$, $\sigma = 357.50$, and $n = 81$, the calculation for the lower limit does not result in $646.50.

The Standard Deviation for the Checking Account Balances Is Assumed