Pregunta
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.
Answer
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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
0.03 ? Round your answer up to the next integer.
Answer
How to enter your answer (opens in new window)
Ask by Higgins Davey. in the United States
Dec 17,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The required sample size is 1808.
Solución

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Como
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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