Question

NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6

. In an earlier study, the population proportion was estimated to be 0.41
.

How large a sample would be required in order to estimate the fraction of people who black out at 6
or more Gs at the 95%
confidence level with an error of at most 0.04
? Round your answer up to the next integer.

Answer 1

To calculate the sample size required to estimate the fraction of people who black out at 6 or more Gs with an error of at most 0.04 and a 95% confidence level, we can use the formula:

n = (Z^2 * p * (1-p)) / E^2

where:
- n is the sample size
- Z is the Z-score for the desired confidence level (1.96 for 95% confidence level)
- p is the estimated population proportion
- E is the desired margin of error (0.04 in this case)

Substituting the given values into the formula, we get:

n = (1.96^2 * 0.41 * (1-0.41)) / 0.04^2
n = 601.67

Rounding up to the nearest integer, we get:

n = 602

Therefore, a sample size of at least 602 is required to estimate the fraction of people who black out at 6 or more Gs with an error of at most 0.04 and a 95% confidence level.