Answer
Confidence interval: $9.499\lt y\lt19.929$
We are 95% confident that the mean sugar content of a energy bar is between 9.499 and 19.929 grams.
Work Step by Step
So, according to the previous item we can not use the least-squares regression equation as we used in the previous problems (7, 8, 9, ...). We will use the methods from section 9.2
In MINITAB, enter the Sugar values in C1.
Select Stats -> Basic Stas -> Display Descriptive Statistics
In Variables enter C1 and click in Statistics.
Select "Mean" and "Standard deviation". Click OK.
Click Ok.
$Mean=y ̅=14.714$ and $s=9.034$
$n=14$, so:
$d.f.=n-1=13$
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$t_{\frac{α}{2}}=t_{0.025}=2.160$
(According to Table VI, for d.f. = 13 and area in right tail = 0.025)
$Lower~bound=y ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=14.714-2.160\times\frac{9.034}{\sqrt {14}}=9.499$
$Upper~bound=y ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=14.714+2.160\times\frac{9.034}{\sqrt {14}}=19.929$
