A local bank needs information concerning the checking accou

A local bank needs information concerning the checking account balances of its customers. A random sample of 15 accounts was checked. The mean balance was $686.75 with a standard deviation of $256.20. Find a 95% confidence interval for the true mean.

Solution

Confidence intervals are used to find a region in which we are 100 * ( 1 - ? )% confident the true value of the parameter is in the interval.
In order for the Confidence Interval to be valid you must have data from a normal distribution, at least if you are using the method here. If you do not have normal data then this type of confidence interval is not valid.

To clear up the notation I will use here. \"t\" is the test statistic and \"t_(n-1)\" is a Student t random variable with n - 1 degrees of freedom, e.g. a Student t random variable with 18 degrees of freedom is denoted as t_18.For small sample confidence intervals about the mean you have:
xBar