Question

Suppose we want to do a study on the body mass index (BMI) on patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared.

1. How many participants would be needed to ensure that a 95% confidence interval estimate of BMI had a margin of error not exceeding 2 units? Assume that the standard deviation of BMI is 5.9 kg/m2.

2. Does the number of participants needed increase or decrease if the margin of error increases?

Answer 1

(1) we have standard deviation (SD) = 5.9

Margin of error (ME) = 2

z score corresponding to 95% confidence interval is 1.96 using normal distribution table

we have to find the value of sample size(n)

using the formula

sample size(n) =

setting the given values, it gives us

Sample size(n) =

so, the required size is n = 33 (rounded to nearest integer)

(2) we have the formula for sample size and margin of error

sample size(n) =

It is clear that the sample size is inversely proportional to the margin of error, i.e. increase in margin of error decreases the sample size and decrease in margin of error increases the sample size.

so, sample size (n) decreases with increase in the margin of error.