Question

In a survey of 2035 workers, 73% reported working out 3 or more days a week. What is the margin of error? What is the interval that is likely to contain the exact percent of all people who work out 3 or more days a week? Show all work.

Your work needs to be your own. If you need help, reach out to your teacher. Use this formula:

Answer 1

To find the margin of error, we need to use the formula:

Margin of Error = z*(sqrt(p*(1-p))/sqrt(n))

where:
z = the z-score associated with a given level of confidence (we'll use 1.96 for 95% confidence)
p = the proportion of the sample with the characteristic of interest (in this case, 0.73)
n = the sample size (2035)

Margin of Error = 1.96*(sqrt(0.73*(1-0.73))/sqrt(2035))
Margin of Error = 0.027

So the margin of error is 0.027 or 2.7%.

To find the interval that is likely to contain the exact percent of all people who work out 3 or more days a week, we need to use the formula:

Interval = Sample Proportion ± Margin of Error

Interval = 0.73 ± 0.027
Interval = (0.703, 0.757)

So we can say with 95% confidence that the true proportion of all people who work out 3 or more days a week is between 70.3% and 75.7%.