Answer
Confidence interval: $111.77\lt β_1\lt163.63$
We are 95% confident that as a 3D television increases by 1 inch its price increases between 111.77 and 163.63 dollars.
Work Step by Step
From item (d):
$\sqrt {∑(x_i-x ̅)^2}=\sqrt {n-1}s_x=\sqrt {9-1}\times8.6747=24.5358$
$n=9$, so:
$d.f.=n-2=7$
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$t_{\frac{α}{2}}=t_{0.025}=2.365$
(According to Table VI, for d.f. = 7 and area in right tail = 0.025)
$Lower~bound=b_1-t_{\frac{α}{2}}\frac{s_e}{\sqrt {Σ(x_i-x ̅)^2}}=137.7-2.365\times\frac{269.049}{24.5358}=111.77$
$Upper~bound=b_1+t_{\frac{α}{2}}\frac{s_e}{\sqrt {Σ(x_i-x ̅)^2}}=137.7+2.365\times\frac{269.049}{24.5358}=163.63$
