Problem 5 Sample Size for a Confidence Interval forTwo Independent Samples Dichotomous OutcomeAn investigator wants to estimate the impact of smoking on the incidence of prostatecancerThe incidence of prostate cancer by the age of 70 is about 1 in 6 (17%) Pz =0. 1U.S. study reported that heavy smokers had twice the risk of developing prostatecancer as compared to nonsmokers (34%) P6.34Repeat study in England, cohort enrolls men at age 50 and followed them for 30yearsWant to generate a 95% confidence level, assume a 20% attrition, and a margin oferror of no more than 0.05 (5%)EFO.0S

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Asked Oct 28, 2019
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Problem 5

Problem 5 Sample Size for a Confidence Interval for
Two Independent Samples Dichotomous Outcome
An investigator wants to estimate the impact of smoking on the incidence of prostate
cancer
The incidence of prostate cancer by the age of 70 is about 1 in 6 (17%) Pz =0. 1
U.S. study reported that heavy smokers had twice the risk of developing prostate
cancer as compared to nonsmokers (34%) P6.34
Repeat study in England, cohort enrolls men at age 50 and followed them for 30
years
Want to generate a 95% confidence level, assume a 20% attrition, and a margin of
error of no more than 0.05 (5%)
EFO.0S
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Problem 5 Sample Size for a Confidence Interval for Two Independent Samples Dichotomous Outcome An investigator wants to estimate the impact of smoking on the incidence of prostate cancer The incidence of prostate cancer by the age of 70 is about 1 in 6 (17%) Pz =0. 1 U.S. study reported that heavy smokers had twice the risk of developing prostate cancer as compared to nonsmokers (34%) P6.34 Repeat study in England, cohort enrolls men at age 50 and followed them for 30 years Want to generate a 95% confidence level, assume a 20% attrition, and a margin of error of no more than 0.05 (5%) EFO.0S

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Step 1

Preliminary information:

Proportion of success in group 1 is p1 is 0.34.

Proportion of success in group 2 is p2 is 0.17.

Margin of error, E=0.05

Using the EXCEL formula “=NORM.S.INV(1-(0.05/2))”, the z-value for 95% confidence level is obtained as 1.96.

Step 2

Computation of number of individuals would need to be included:

The number of individuals would need to be included in...

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n={p(1-P)+P(1-p 1.96 ={0.34(1-0.34)+0.17(1-0.17); 0.05 0.3655x1,536.64 561.64 - 562

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