Pregunta
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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 0.43 .
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 confidence level with an error of at most
0.03 ? Round your answer up to the next integer.
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Ask by Higgins Davey. in the United States
Dec 17,2024

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The required sample size is 1808.

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Bonus Knowledge

To find the required sample size, you can use the formula for the sample size for estimating a population proportion:
where:
  • is the Z-score corresponding to the desired confidence level,
  • is the estimated population proportion,
  • is the margin of error.
For a confidence level of , the Z-score is approximately . Given and :
Rounding up, the required sample size is .
First Additional Information: Fun fact! The phenomenon of humans blacking out under high G forces is utilized in training for both pilots and astronauts. They engage in G-force simulations to get accustomed to the sensation and the coping mechanisms needed to withstand intense acceleration, which can occur in jet fighters or space launch scenarios!
Second Additional Information: If you’re keen to explore further, a fascinating realm of research focuses on the physiological adaptations humans develop in response to increased G forces. Countermeasures like anti-G suits and specific breathing techniques are designed to help pilots maintain consciousness, illustrating our incredible human capacity to adapt to extreme conditions!

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