In this case the population standard deviation is unknown. We only have the sample standard deviation s. Then,
the confidence interval formula for estimating the population mean is
[tex]\bar{x}-T_c\frac{s}{\sqrt[]{n}}<\mu<\bar{x}+Tc\frac{s}{\sqrt[]{n}}[/tex]
where Tc is the critical T-value, which depends on the confidence level. For the 95% confidence level and n=26, the T value is
[tex]T_C=2.060[/tex]
Then, by substituting this value and the given ones into the confidence interval, we have
[tex]37-(2.060)\frac{11}{\sqrt[]{26}}<\mu<37+(2.060)\frac{11}{\sqrt[]{26}}[/tex]
which gives
[tex]37-4.44399<\mu<37+4.44399[/tex]
By rounding to 3 decimal places, the answer is
[tex]32.556<\mu<41.444[/tex]
