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

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to Biostat Chapter 8:Example 6.

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

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for one-sample dichotomous outcome

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to perform hypothesis testing.

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The problem here is not from our textbook,

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and first I will read the problem.

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The issue here is that we have performed an intervention

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for older adult females to improve their bone health.

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From published literature, we have been able to determine

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that bone fracture for similar population is 63%.

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We are hypothesizing that after the intervention,

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bone health will improve.

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Hence we will see a reduction in fracture down to 59%.

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We want to test the hypothesis

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that with a 90% statistical power,

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if there is a true difference in bone fracture

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after the intervention. How many subjects are required?

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So here I have provided you

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with all the information in a summary format,

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and I have also inserted the formula here.

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And now, as we move forward, we first need

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to determine the effect size, and for the effect size,

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the numerator here is the difference

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between the hypothesized value and the established value.

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And the denominator is the square root

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of the established value multiplied by one minus that value.

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So here I have inserted all the values

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as they were provided in the problem,

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and after that, once we perform the algebra, we get

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that the effect size is equal to 0.083.

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Now we have to determine the other values that

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we need to insert in the formula

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to determine our sample size.

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So the value for Z1 minus alpha divided by two.

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The Z 97.5th percentile is 1.96,

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which is a value we have used multiple times by now.

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The value of Z one minus beta here would be

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the Z 90th percentile because one minus beta

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is the power of the study,

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and that is going to be 1.282.

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So now we will insert these values

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and once we insert these values

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and perform the algebra,

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we get 1528.81.

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So once we round it up, we get 1,529.

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So 1,529 subjects are required.