$n = 12 , \bar { x } = 28.0 , s = 5.7$. Find a $99 \%$ confidence interval for the mean.
A) $( 22.79,33.21 )$
B) $( 22.89,33.11 )$
C) $( 22.79,33.09 )$
D) $( 22.91,33.09 )$
E) $( 23.53,32.47 )$

Question

Quizplus · Accepted Answer

The 99% confidence interval for the mean is calculated using the formula $\bar{x} \pm t^* \frac{s}{\sqrt{n}}$. For $n = 12$, the degrees of freedom is 11. The critical value $t^*$ for 99% confidence and 11 degrees of freedom is approximately 3.106. Thus, the interval is $28.0 \pm 3.106 \times \frac{5.7}{\sqrt{12}}$, which results in $(22.89, 33.11)$.

n=12,xˉ=28.0,s=5.7n = 12 , \bar { x } = 28.0 , s = 5.7n=12,xˉ=28.0,s=5.7

$n = 12 , \bar { x } = 28.0 , s = 5.7$