Answer
Confidence interval: $98.86\lt x ̅\lt109.74$
As the sample size increases, the width of the interval decreases.
Work Step by Step
$n=25$, so:
$d.f.=n-1=24$
$level~of~confidence=(1-α).100$%
$90$% $=(1-α).100$%
$0.9=1-α$
$α=0.1$
$t_{\frac{α}{2}}=t_{0.05}=1.711$
(According to Table VI, for d.f. = 24 and area in right tail = 0.05)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=104.3-1.711\times\frac{15.9}{\sqrt {25}}=98.86$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=104.3+1.711\times\frac{15.9}{\sqrt {25}}=109.74$
