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.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.4: Discrete Random Variables; Applications To Decision Making

Problem 10E

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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.

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