The sample space of a population being researched contains 58 values and a mean of 318.6. the population has a known standard deviation of 29.2. identify the margin of error for a 95% confidence interval estimate of the mean of the population.

We have the following data:

Sample size = n = 58

Sample mean = x = 318.6

Population Standard Deviation = s = 29.2

Confidence Level = 95%

Since the population standard deviation is known, we can use z distribution to find the critical values for the 95% confidence interval. The z value from z table for 95% confidence interval comes out to be

z = 1.96

The confidence interval for the population mean will be:

Using the values of all the variables, we get:

Thus the 95% confidence interval about the population mean is (311.09 , 326.11).

Conclusion:

We are 95% confident that the true value of population means is between the bounds of the confidence interval i.e. between 311.09 and 326.11

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