A process that cuts lengths of metal with high precision has historically produced metal rods with length that is normally distributed and with a mean of 800 millimetres (mm). Management at the factory is concerned that after an overhaul of the machine the mean length of the rods being produced could differ from the required 800 mm. If it is found that the rods are not being produced to specifications then the machine will have to be stopped for readjustment, with a consequent loss of production. The production line manager tasked with investigating the issue finds that a (random) sample of 25 rods yielded a mean length of 806 mm and a sample standard deviation of 10 mm. i. The mean of the sample is clearly not the required 800 mm. Say why this is not enough information in itself to say if the machine is operating correctly or not. ii. State the null and alternative hypotheses for this situation.
. A process that cuts lengths of metal with high precision has historically produced metal
rods with length that is
Management at the factory is concerned that after an overhaul of the machine the mean
length of the rods being produced could differ from the required 800 mm. If it is found that
the rods are not being produced to specifications then the machine will have to be stopped
for readjustment, with a consequent loss of production. The production line manager tasked
with investigating the issue finds that a (random) sample of 25 rods yielded a mean length
of 806 mm and a sample standard deviation of 10 mm.
i. The mean of the sample is clearly not the required 800 mm. Say why this is not enough
information in itself to say if the machine is operating correctly or not.
ii. State the null and alternative hypotheses for this situation.
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