“Red tide” is a bloom of poison-producing algae—a few different species of a class of plankton called dinoflagellates. When the weather and water conditions cause these blooms, shellfish such as clams living In the area develop dangerous levels of a paralysis-inducing toxin. In Massachusetts. the Division of Marine Fisheries (DMF) monitors levels of the toxin in shellfish by regular sampling of shellfish along the coastline. If the mean level of toxin in clams exceeds 800 pg (micrograms) of toxin per kg of clam meat In any area, clam harvesting Is banned there until the bloom Is over and levels of toxin in clams subside. Describe both a Type I and a Type II error In this context, and state which error has the greater consequence.
“Red tide” is a bloom of poison-producing algae—a few different species of a class of plankton called dinoflagellates. When the weather and water conditions cause these blooms, shellfish such as clams living In the area develop dangerous levels of a paralysis-inducing toxin. In Massachusetts. the Division of Marine Fisheries (DMF) monitors levels of the toxin in shellfish by regular sampling of shellfish along the coastline. If the mean level of toxin in clams exceeds 800 pg (micrograms) of toxin per kg of clam meat In any area, clam harvesting Is banned there until the bloom Is over and levels of toxin in clams subside. Describe both a Type I and a Type II error In this context, and state which error has the greater consequence.
“Red tide” is a bloom of poison-producing algae—a few different species of a class of plankton called dinoflagellates. When the weather and water conditions cause these blooms, shellfish such as clams living In the area develop dangerous levels of a paralysis-inducing toxin. In Massachusetts. the Division of Marine Fisheries (DMF) monitors levels of the toxin in shellfish by regular sampling of shellfish along the coastline. If the mean level of toxin in clams exceeds 800 pg (micrograms) of toxin per kg of clam meat In any area, clam harvesting Is banned there until the bloom Is over and levels of toxin in clams subside. Describe both a Type I and a Type II error In this context, and state which error has the greater consequence.
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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