What is the 95% confidence interval for the mean noise level in the operating rooms, based on a sample of 4 operating rooms with a mean noise level of 39.4 decibels and a standard deviation of 11.9 decibels?

Question

15-02-2025
Mathematics

High School

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What is the 95% confidence interval for the mean noise level in the operating rooms, based on a sample of 4 operating rooms with a mean noise level of 39.4 decibels and a standard deviation of 11.9 decibels?

Answer :

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Final answer:

To calculate the 95% confidence interval for the mean noise level in the operating rooms, use the formula CI = mean ± (Z * (standard deviation / √n)). Plugging in the given values, the 95% confidence interval is (27.74, 51.06) decibels.

Explanation:

To calculate the 95% confidence interval for the mean noise level in the operating rooms, you can use the formula:

CI = mean ± (Z * (standard deviation / √n))

Where CI is the confidence interval, mean is the sample mean noise level, Z is the Z-score corresponding to the desired confidence level (1.96 for a 95% confidence level), standard deviation is the sample standard deviation, and n is the sample size.

Plugging in the given values, we get:

CI = 39.4 ± (1.96 * (11.9 / √4)) = 39.4 ± (1.96 * 5.95) = 39.4 ± 11.66

The 95% confidence interval for the mean noise level in the operating rooms is (27.74, 51.06) decibels.

Learn more about confidence interval here:

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