The concentration of a particular chemical in a processing plant is monitored regularly to check that it remains near the desired level of 8.25 mmol/L. Because of variability in the measurement system, this is checked by taking multiple samples over a short period of time and using the resulting measurements to carry out a formal statistical test. (The null hypothesis for this test is that the true mean concentration of the chemical is equal to the desired value, and you may assume that the measurements are Normally distributed.)
The concentration of a particular chemical in a processing plant is monitored regularly to check that it remains near the desired level of 8.25 mmol/L. Because of variability in the measurement system, this is checked by taking multiple samples over a short period of time and using the resulting measurements to carry out a formal statistical test. (The null hypothesis for this test is that the true mean concentration of the chemical is equal to the desired value, and you may assume that the measurements are Normally distributed.)
The concentration of a particular chemical in a processing plant is monitored regularly to check that it remains near the desired level of 8.25 mmol/L. Because of variability in the measurement system, this is checked by taking multiple samples over a short period of time and using the resulting measurements to carry out a formal statistical test. (The null hypothesis for this test is that the true mean concentration of the chemical is equal to the desired value, and you may assume that the measurements are Normally distributed.)
The concentration of a particular chemical in a processing plant is monitored regularly to check that it remains near the desired level of 8.25 mmol/L. Because of variability in the measurement system, this is checked by taking multiple samples over a short period of time and using the resulting measurements to carry out a formal statistical test. (The null hypothesis for this test is that the true mean concentration of the chemical is equal to the desired value, and you may assume that the measurements are Normally distributed.)
The latest sample of eight measurements gave a sample average concentration (X) of 8.13 mmol/L and a sample standard deviation (s) of 0.16 mmol/L. Use this information and the statistical tables provided on Canvas to carry out the statistical test mentioned above, and report on what evidence (if any) there is to suggest that the mean concentration of the chemical has varied from the desired level.
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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