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<v Instructor>Hello students, and welcome</v>

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to Biostat ER Chapter 8: Example 2.

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In this example, we will learn how to calculate sample size

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for one sample continuous outcome

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to determine confidence interval,

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and we will utilize the data from example one.

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The problem statement hence is going to be the same,

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but I will read it again.

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The issue here is that we have collected some data,

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and we need to know if our sample mean is different

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from some established mean, which is 100.

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We want a hypothesis test with 80% power,

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and we know that we will fail

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to reject the null hypothesis

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within a margin of error of five.

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Therefore, if our mean is between 95

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and 105, we know that we will fail

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to reject the null hypothesis.

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From publications for similar studies,

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we know that the standard deviation is between 8.5 and 9.5.

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So the question is how many subjects are required

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to determine a confidence interval that will have a margin

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of error no greater than five?

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So again, for your convenience,

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I have summarized the information here,

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as you can take a look at it very quickly.

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And I want to also emphasize

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that the Z value here is again going to be 1.96.

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I've also inserted the formula here,

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and it is N equal to Z times sigma divided

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by E and the whole square.

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Now the standard deviation,

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which was obtained from previous literature is a range,

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and we want to use the highest value

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as it'll give us the most variation

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and ensure that we have enough subjects in the study.

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We are here erroring on the side of caution,

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and we want to ensure that we are enrolling enough people.

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So once we insert all the values, so here Z is going

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to be 1.96, sigma is going to be 9.5,

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the E is going to be five.

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So we insert all the values and we perform the algebra,

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we get 13.9.

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And as always, we are going to round it up

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and that's going to be 14.

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So 14 subjects here are required.