Respuesta :
The minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268
Given: To find the minimum sample size, confidence level = 99%, standard deviation = 13.8, and one unit population mean. [Normally distributed]
Solving the given question:
We know that the formula for Margin of error is:
Margin of error = z-score * (standard deviation) / root (sample size)
E = z * σ / √(n), where
E = Margin of error
z = z-score
n = Sample size
σ = standard deviation
Therefore, sample size = ( z – score * standard deviation / margin of error)²
n = ( z * σ / E )²
First, calculate the z-score for the 99% confidence level.
From the normal distribution curve, the area under 99% confidence level is given as:
Area under 99% confidence level = (1 + confidence level) / 2 = (1 + 0.99) / 2 = 0.995
From the z-score table, we find the value of z with the corresponding area of 0.995
We find the value of the z-score corresponding to 0.995 is 2.58
Also given sample mean is one unit of the population. So the margin of error is 1
E = 1
And given Standard deviation = 13.8
σ = 13.8
Putting the values in the given formula of sample size n =
n = (2.58 * 13.8 / 1 )²
n = 1267.64
n = 1268
Hence the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268
Know more about “normal distribution” here: https://brainly.com/question/15103234
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Disclaimer: Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and G = 13.8. Assume the population is normally distributed. A 99% confidence level requires a sample size of (Round up to the nearest whole number as needed )
