Answer
There is no evidence to conclude that the boxed version performs better than the traditional roll.
Since the traditional roll has a significantly lower price than the boxed version with a performance of about the same than the boxed version, it is recommended to buy the traditional roll.
Work Step by Step
$x ̅_1,n_1~and~s_1$ refer to the boxed version and $x ̅_2,n_2~and~s_2$ refer to the roll.
$t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(0.9717-1.0200)-0}{\sqrt {\frac{0.0538^2}{6}+\frac{0.0942^2}{6}}}=-1.091$
Left-tailed test:
$n=6$ (use the smaller value of $n$), so:
$d.f.=n-1=5$
$P$-value $=P(t\lt t_0)=P(t\lt-1.091)=P(t\gt1.091)$
For $d.f.=5$ and the area to area in right tail equals to 0.15: $t=1.156$
For $d.f.=5$ and the area to area in right tail equals to 0.20: $t=0.920$
So, $0.15\lt P$-value $\lt0.20$.
Since $P$-value $\gt α$, for any usual $α$ (0.01, 0.05, 0.10), we do not reject the null hypothesis.
