Both of your confidence interval limits are incorrect. The confidence interval for the estimate of

muμ

is

x overbar minus Upper E less than mu less than x overbar plus Upper Ex−E<μ<x+E​,

where E is the margin of​ error, and

x overbarx

is the sample mean. The margin of error is given by the formula​ below, where

t Subscript alpha divided by 2tα/2

is the critical t value separating an area of

alpha divided by 2α/2

in the right tail of the Student t​ distribution, and

dfequals=nminus−1

is the number of degrees of freedom.

Upper E equals t Subscript alpha divided by 2 Baseline times StartFraction s Over StartRoot n EndRoot EndFraction left parenthesis Use df equals n minus 1 right parenthesisE=tα/2•sn   (Use df=n−1)

If using a table of critical​ t-values to find a critical value of

t Subscript alpha divided by 2tα/2​,

but the table does not include the number of degrees of​ freedom, the closest value could be​ used, the next lower number of degrees of freedom found in the table could be used as a conservative​ value, or interpolation could be used.

​Alternatively, technology can be used to find the confidence interval. Make sure to round to one decimal place.