Using the Formula for Margin of Error When Estimating a Population Mean - dummies

# Using the Formula for Margin of Error When Estimating a Population Mean

For these three sample questions, consider that: A researcher conducted an Internet survey of 300 students at a particular college to estimate the average amount of money students spend on groceries per week. The researcher knows that the population standard deviation of weekly spending is \$25. The mean of the sample is \$85.

The following table provides the z*- values for selected (percentage) confidence levels.

## Sample questions

1. What is the margin of error if the researcher wants to be 99% confident of the result?

The formula for margin of error when estimating a population mean is

where z* is the value from the table for a given confidence level (99% in this case, or 2.58),

is the standard deviation (\$25), and n is the sample size (300).

Now, substitute the values into the formula and solve:

The margin of error for a 99% confidence interval for the population mean is plus/minus \$3.72.

2. What is the margin of error if the researcher wants to be 95% confident in the result?

The formula for margin of error when estimating a population mean is

where z* is the value from the table for a given confidence level (95% in this case, or 1.96),

is the standard deviation (\$25), and n is the sample size (300).

Now, substitute the values into the formula and solve:

The margin of error for a 95% confidence interval for the population mean is plus/minus \$2.83.

3. What is the lower limit of an 80% confidence interval for the population mean, based on this data?