Question
please get it right
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 0.4
.
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 98%
confidence level with an error of at most 0.04
? Round your answer up to the next integer.
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 0.4
.
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 98%
confidence level with an error of at most 0.04
? Round your answer up to the next integer.
Answers
GPT 3.5
To calculate the sample size required for this experiment, we can use the formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = Z-score for 98% confidence level, which is approximately 2.33
p = estimated population proportion = 0.4
E = margin of error = 0.04
Plugging in the values, we get:
n = (2.33^2 * 0.4 * 0.6) / 0.04^2
n = (5.4289 * 0.24) / 0.0016
n = 1.29936 / 0.0016
n = 811
So, a sample size of 811 would be required in order to estimate the fraction of people who black out at 6 or more Gs at the 98% confidence level with an error of at most 0.04. Since sample sizes must be whole numbers, we round up to the next integer, giving a final answer of 812.
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = Z-score for 98% confidence level, which is approximately 2.33
p = estimated population proportion = 0.4
E = margin of error = 0.04
Plugging in the values, we get:
n = (2.33^2 * 0.4 * 0.6) / 0.04^2
n = (5.4289 * 0.24) / 0.0016
n = 1.29936 / 0.0016
n = 811
So, a sample size of 811 would be required in order to estimate the fraction of people who black out at 6 or more Gs at the 98% confidence level with an error of at most 0.04. Since sample sizes must be whole numbers, we round up to the next integer, giving a final answer of 812.