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 O- ring 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 O- ring 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 O- ring 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 O- ring 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.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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