How can I find the true mean?

Question

Noise levels at various area urban hospitals were measured in decibels. The mean noise level in 169 ward areas was 61.6 decibels, and the population standard deviation is 4.7. Find the 95% confidence interval of the true mean. Round the answers to one decimal place.

Answer 1

Since the sample size (n) is ≥ 30, we will assume the data to be normally distributed.

Here, n = 169, σ (standard deviation) = 4.7, and the mean, xbar = 61.6 decibels

First, we need to calculate the error,E, which is given by:

E = zσ/√n, where z is the critical value obtained from the z table for 95% level of confidence.

From the z table, z (0.95) = 1.96

Thus, E = (1.96*4.7)/√169

E = 0.7086

The true mean lies in the interval xbar - E<μ<xbar + E

61.6-0.7086<μ<61.6+0.7086 at 95% confidence level

60.8914<μ<62.3086 OR 60.9<μ<62.3

Thus, there is a 95% chance that the true mean (population) noise level in the hospital ward areas lies in the interval 60.9 to 62.3 decibels.