Pleasantville Steel Works stamps/produces O-rings for various metal-work companies. The metal-work companies expect the O-rings to have a diameter of 30 cm. The machine that makes these O-rings does not always produce each Oring with a diameter of exactly 30 cm (sometimes, metal shards are left behind after pressing and affect the next O-ring) and consequently, the O-rings can vary slightly. When the machine is working properly, the O-rings made on this machine have a mean diameter of exactly 30 cm. The standard deviation of the diameters of all O-rings produced on this machine is always equal to 0.5 mm. The quality control department takes a random sample of 35 such O-rings every week, calculates the mean of those diameters for these O-rings, and makes a 99% confidence interval for the population mean. If either the lower limit of this confidence interval is less than 29.9500 cm or the upper limit of this confidence interval is greater than 30.04 cm, the machine must be stopped and re-calibrated/adjusted. During the 1st week of March 2021, a sample of 35 rings produced a mean diameter of 30.0250 cm. Based on this sample, can you conclude that the machine needs (or doesn’t need) to be re-calibrated/adjusted? Explain/justify your conclusion.
Pleasantville Steel Works stamps/produces O-rings for various metal-work
companies. The metal-work companies expect the O-rings to have a diameter of
30 cm. The machine that makes these O-rings does not always produce each Oring with a diameter of exactly 30 cm (sometimes, metal shards are left behind
after pressing and affect the next O-ring) and consequently, the O-rings can vary
slightly.
When the machine is working properly, the O-rings made on this machine have a
mean diameter of exactly 30 cm. The standard deviation of the diameters of all
O-rings produced on this machine is always equal to 0.5 mm. The quality control
department takes a random sample of 35 such O-rings every week, calculates the
mean of those diameters for these O-rings, and makes a 99% confidence interval
for the population mean. If either the lower limit of this confidence interval is
less than 29.9500 cm or the upper limit of this confidence interval is greater than
30.04 cm, the machine must be stopped and re-calibrated/adjusted. During the
1st week of March 2021, a sample of 35 rings produced a mean diameter of
30.0250 cm.
Based on this sample, can you conclude that the machine needs (or doesn’t need)
to be re-calibrated/adjusted? Explain/justify your conclusion.
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