Suppose that the amount of time a laboratory worker takes to complete a particular task is approximately distributed with a known mean of 205 and a known standard deviation of 21. A new protocol for completing the task has been suggested, that is believed to reduce the mean time until completion of the task. Use this information to answer the following.
Suppose that the amount of time a laboratory worker takes to complete a particular task is approximately distributed with a known mean of 205 and a known standard deviation of 21. A new protocol for completing the task has been suggested, that is believed to reduce the mean time until completion of the task. Use this information to answer the following.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Transcribed Image Text:Suppose that the amount of time a laboratory worker takes to complete a particular task is approximately
distributed with a known mean of 205 and a known standard deviation of 21. A new protocol for completing
the task has been suggested, that is believed to reduce the mean time until completion of the task. Use this
information to answer the following.
Transcribed Image Text:Part (d) (WebWorkiR) Suppose it is desirable to have a 85% power of detecting a decrease of 10 seconds
in the mean completion time under the new protocol, while using the same hypotheses and significance
level in previous questions. What sample size would be necessary? Please round your answer up to the
nearest whole number.
Expert Solution
Step 1: Description of formula of sample size:
The sample size for a hypothesis test of the difference between means depends on the desired level of significance (alpha), power (1 - beta), the effect size, and the standard deviation of the population. The formula for the sample size is:
n = (Zα/2 + Zβ)² * σ² / δ²
Where,
Zα/2 is the critical value of the standard normal distribution for the level of significance alpha.
Zβ is the critical value of the standard normal distribution for the power.
σ is the standard deviation of the population.
δ is the effect size, which is the difference between the means divided by the standard deviation of the population.
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