Calculate the margin of error for a 99% confidence interval given the sample size, sample standard deviation, and confidence level. What is given in the problem?
Sample size: n = 36
Sample standard deviation: s = 10
Confidence level: 99%.
Answer (2)
The margin of error for a 99% confidence interval, given a sample size of 36 and a sample standard deviation of 10, is approximately 4.30. This is calculated using the z-score for 99% confidence and the standard error of the mean. The final margin of error reflects the range within which we expect the true population parameter to fall based on the sample data.
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To calculate the margin of error for a 99% confidence interval, you will follow these steps:
Identify the appropriate Z-score:
For a 99% confidence interval, the Z-score (which represents the standard normal distribution) is approximately 2.576.
Use the formula for the margin of error (ME):
The margin of error is calculated using the formula:
ME = Z × ( n s )
where:
Z is the Z-score for your confidence level.
s is the sample standard deviation.
n is the sample size.
Plug in the given values:
Sample standard deviation, s = 10
Sample size, n = 36
Z-score for a 99% confidence level, Z = 2.576
Calculate the standard error (SE):
The standard error is calculated as:
SE = n s = 36 10 = 6 10 ≈ 1.667
Calculate the margin of error:
Substitute the values into the margin of error formula:
ME = 2.576 × 1.667 ≈ 4.29
Therefore, the margin of error for a 99% confidence interval given the sample size, sample standard deviation, and confidence level is approximately 4.29.
