Download Margin of Error and Confidence Intervals

a
fixed measure for a given
population
 ie: Mean, variance, or standard
deviation
a
single value estimate of a
population parameter based on
sample

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.

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.

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.

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.

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%?

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%?

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?

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.

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.

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.