Answer
Confidence interval: $46.3\lt x ̅\lt53.7$
Compared to the results obtained in part (a), the margin of error has decreased.
Work Step by Step
$n=20$, so:
$d.f.=n-1=19$
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$t_{\frac{α}{2}}=t_{0.025}=2.093$
(According to Table VI, for d.f. = 19 and area in right tail = 0.025)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=50-2.093\times\frac{8}{\sqrt {20}}=46.3$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=50+2.093\times\frac{8}{\sqrt {20}}=53.7$
