Answer
$t_0\gt t_α$: null hypothesis is rejected.
There is enough evidence to conclude that gas in Chicago more expensive than the nation.
Work Step by Step
$H_0:~µ=3.101$ versus $H_1:~µ\gt3.101$
$x ̅_1=\frac{∑x_{1_i}}{n_1}=3.1595$
$s_1=\sqrt {\frac{∑(x_{1_i}-x ̅_1)^2}{n_1-1}}=0.06599$
Requirement:
The population was extracted from a sample that is normally distributed with no outliers.
$n=21$, so:
$d.f.=n-1=20$
$t_0=\frac{x ̅-µ_0}{\frac{s}{\sqrt n}}=\frac{3.1595-3.101}{\frac{0.06599}{\sqrt {21}}}=4.062$
Let's use $α=0.01$ level of significance.
$t_α=t_{0.01}=2.528$
(According to Table VI, for d.f. = 20 and area in right tail = 0.01)
Since $t_0\gt t_α$, we reject the null hypothesis.
Notice that the null hypothesis would be rejected even for the $α=0.05$ or $α=0.10$ level of significance. They would provide a lower value of $t_α$.
