A machine is set to fill packets with 1000 g of flour on average. The manager wants to check whether the machine is overfilling or underfilling the packets. If \(\mu\) is the mean weight (in g) of the packets, the test to be used and the alternative hypothesis are
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → a two-tailed test with \(H_1: \mu \ne 1000\)
The null hypothesis is the setting of the machine:
\(H_0: \mu = 1000\)
The manager looks for a difference in either direction (too much or too little), so
\(H_1: \mu \ne 1000\)
Such a test rejects \(H_0\) for values of t far out in either tail, so it is a two-tailed test.
A left-tailed or right-tailed test would look for underfilling only or overfilling only, and \(\mu = 1000\) is the null hypothesis, not the alternative.