To confirm the effectiveness of some medicine, its concentration in blood must exceed 400 ppm (parts per million). The analyst in a laboratory generates 5 identical specimens taken from a blood sample and tests them using some device. Assuming a significance level of 2%, answer the following:If the standard deviation of the medicine concentrations was 50 ppm and their mean was 450 ppm, test the hypothesis that the medicine is effective.If the laboratory used another device and did 5 more tests and reported that the standard deviation of the results became 10 ppm. Test if the quality control (degree of variation) of the new device is better than the old device.Based only on the new standard deviation of 10 ppm, compute the minimum required mean value for the 5 samples such that the effectiveness of the medicine is confirmed.Using the combined data (the old 5 tests + the new 5 tests) re-test the hypothesis that that the medicine is effective.Based on data from large population, the true mean is in fact 390 ppm, calculate the probability of making type II error in part a)

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Description: To confirm the effectiveness of some medicine, its concentration in blood must exceed 400 ppm (parts per million). The analyst in a laboratory generates 5 identical specimens taken from a blood sample and tests them using some device. Assuming a sig

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To confirm the effectiveness of some medicine, its concentration in blood must exceed 400 ppm (parts per million). The analyst in a laboratory generates 5 identical specimens taken from a blood sample and tests them using some device. Assuming a significance level of 2%, answer the following:

If the standard deviation of the medicine concentrations was 50 ppm and their mean was 450 ppm, test the hypothesis that the medicine is effective.
If the laboratory used another device and did 5 more tests and reported that the standard deviation of the results became 10 ppm. Test if the quality control (degree of variation) of the new device is better than the old device.
Based only on the new standard deviation of 10 ppm, compute the minimum required mean value for the 5 samples such that the effectiveness of the medicine is confirmed.
Using the combined data (the old 5 tests + the new 5 tests) re-test the hypothesis that that the medicine is effective.
Based on data from large population, the true mean is in fact 390 ppm, calculate the probability of making type II error in part a)

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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