Answer
Since we fail to reject the Null hypothesis, we can conclude that the service time has not decreased.
Work Step by Step
Here we have $H_{o}$: μ = 167.1, $H_{1}$: μ < 167.1, n = 70, x̅ = 163.9,
s = 15.3 and α = 0.01
Using the Classical approach:
Using Table VI, we have: t = 2.390
Rejection region < -2.390
$σ_{ x̅} = \frac{s}{\sqrt n} = \frac{15.3}{\sqrt 70} = 1.83$
$t = \frac{163.9 - 167.1}{1.83} = -1.749$
Since, -1.749 > -2.390, we do not reject the Null hypothesis.
