Margin of Error and Confidence Intervals

a fixed measure for a given population

ie: Mean, variance, or standard deviation

Population Parameter:

a single value estimate of a population parameter based on sample

Point Estimate

the greatest possible distance between the value of a population parameter and a point of estimate;

where is the z-score that corresponds to the confidence level, c, σ is the population standard deviation, n is the sample size and E is the margin of error.

Margin of Error “E”

the estimate of a population parameter on an interval with a certain probability that the population parameter lies within that interval; the confidence interval for the population mean, µ, is:

where is the sample mean and E is the margin of error of the population mean.

Confidence Interval

The method used to find the range in either direction of the average. We will use the calculator to determine the mean and the standard deviation. We will then use the z – table (confidence level) with these two numbers to calculate our margin of error. We will multiply the z – table by the quotient of the standard deviation and the square root of the sample space.

In laymen’s terms:

Once we have the margin of error, we will take the mean minus the margin of error and the mean plus the margin of error. This will give us our confidence interval.

In laymen’s terms (cont.):

Given a sample mean of 15.5 and a sample standard deviation of 2.3, what would the margin of error be if the sample data set consisted of 90 items with a confidence level of 80%?

Example 1

Given a sample mean of 95.7 and a sample standard deviation of 4.8, what would the margin of error be if the sample data set consisted of 50 items with a confidence level of 96%?

Example 2

Company A states that their product keeps food cold for 8 hours without ice. A research company completed 350 tests with results of a sample mean of 8.1 hours, a sample standard deviation of 0.56, and a confidence level of 96%. What can be concluded about Company A’s marketing?

Example 3

What is the confidence interval for the population mean if the sample mean is 44.9, the sample standard deviation is 0.87, and the confidence level is 95%? There are 60 items in the sample data set.

Example 4

What is the confidence interval for the population mean if the sample mean is 36.15, the sample standard deviation is 0.98, and the confidence level is 90%? There are 90 items in the sample data set.

Example 5

What is the confidence interval for the population mean if the sample mean is 154.3, the sample standard deviation is 8.0, and the confidence level is 96%? There are 140 items in the sample data set.

Example 6