Define the following terms that are used in hypothesis testing, explaining how they relate to Type I and Type II errors. The significance level of the test. The power of the test. A medial machine at a hospital is regulated so that the amount of drug dispensed is normally distributed with standard deviation 15 µl. It is intended that the mean amount dispensed should be 200 µl. To test whether the machine is working correctly, it is checked periodically by taking a random sample of 9-replicates and calculating the mean amount dispensed. The machine is considered to be working satisfactorily if this mean lies between 191 µl and 209 µl. Write down appropriate null and alternative hypotheses for this testing procedure. State the distribution of the sample mean if the null hypothesis is true. (3marks) Calculate the significance level of the test. If you were performing the test at the 5% level of significance, what would you conclude? Calculate the power of the test if the true mean amount dispensed is 205 ml. Without performing any further calculations, state how you would expect this value to compare with the power of the test if the true mean amount dispensed is 210 µl, justifying your answer.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Define the following terms that are used in hypothesis testing, explaining how they relate to Type I and Type II errors.
The significance level of the test.
The power of the test.
A medial machine at a hospital is regulated so that the amount of drug dispensed is normally distributed with standard deviation 15 µl. It is intended that the mean amount dispensed should be 200 µl. To test whether the machine is working correctly, it is checked periodically by taking a random sample of 9-replicates and calculating the mean amount dispensed. The machine is considered to be working satisfactorily if this mean lies between 191 µl and 209 µl.
Write down appropriate null and alternative hypotheses for this testing procedure.
State the distribution of the sample mean if the null hypothesis is true. (3marks)
Calculate the significance level of the test. If you were performing the test at the 5% level of significance, what would you conclude?

Calculate the power of the test if the true mean amount dispensed is 205 ml. Without performing any further calculations, state how you would expect this value to compare with the power of the test if the true mean amount dispensed is 210 µl, justifying your answer.

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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