$n = 10 , \bar { x } = 13.0 , s = 4.5$. Find a $95 \%$ confidence interval for the mean.
A) $( 9.80,16.20 )$
B) $( 9.78,16.22 )$
C) $( 10.39,15.61 )$
D) $( 9.83,16.20 )$
E) $( 9.83,16.17 )$

Question

Quizplus · Accepted Answer

The 95% confidence interval for the mean is calculated using the formula $\bar{x} \pm t^* \frac{s}{\sqrt{n}}$. For $n = 10$, the degrees of freedom is 9. Using a t-table, the critical value $t^*$ for 95% confidence is approximately 2.262. Thus, the interval is $13.0 \pm 2.262 \times \frac{4.5}{\sqrt{10}}$, which calculates to approximately $(9.78, 16.22)$.

n=10,xˉ=13.0,s=4.5n = 10 , \bar { x } = 13.0 , s = 4.5n=10,xˉ=13.0,s=4.5

$n = 10 , \bar { x } = 13.0 , s = 4.5$