Answer
Since we have rejected the Null hypothesis, this implies that machine is not filling bottles correctly. Hence, the assembly line should be shut down so that the machine can be recalibrated.
Work Step by Step
Here we have: $H_{o}$: μ = 64.05, $H_{1}: μ \ne 64.05$, n = 22, x̅ = 64.007, s = 0.045 and α = 0.01
Using the Classical approach:
Using Table VI, we have: t = +/- 2.831
Since this is a two-tailed test, the rejection region will be values smaller than -2.831 and greater than 2.831.
$σ_{ x̅} = \frac{s}{\sqrt n} = \frac{0.045}{\sqrt 22} = 0.0096$
$t = \frac{64.01 - 64.05}{0.0096} = -4.169$
Since, -4.169 < -2.831, we reject the Null hypothesis.
