header

Confidence Interval Examples

Example 1

According to the National Institutes of Health (NIH), a person is obese if his or her body mass index (BMI) is 30 or above. In a simple random sample of 800 college-age adults (18-24), 10% of the subjects were found to be obese. Find a 90% confidence interval for the proportion of all college-age adults who are obese.

This sample clearly meets the requirements for calculating a confidence interval for the population proportion. The number of successes (10% of 800 = 80) and the number of failures (720) both exceed 15. The number of college-age adults in the country certainly exceeds 8000 (10 times the sample size).

We can state with 90% confidence that the proportion of college-age adults who are obese is between 8.3% and 11.7% (or, put another way, 10% with a margin of error of ± 1.7%).

Using the TI-83

1.645 0.1 0.9 800 calculates the margin of error and stores it as M (you could use any variable but I chose M for margin of error).

0.1 calculates the lower bound of the interval by subtracting the margin of error from the sample proportion.

0.1 calculates the upper bound of the interval by adding the margin of error to the sample proportion.

Using Some Other Calculators

1.645 * ( 0.1 * 0.9 / 800 ) sqrt=MS calculates the margin of error and stores it in memory.

0.1 - MR = calculates the lower bound of the interval by subtracting the margin of error from the sample proportion.

0.1 + MR = calculates the upper bound of the interval by adding the margin of error to the sample proportion.

 

Example 2

In a national survey of 6,000 men aged 50 to 64, 22% of the men indicated that they had participated in binge drinking within the last month. Find a 95% confidence interval for the proportion of men aged 50 to 64 who participated in binge drinking within the last month.

This sample clearly meets the requirements for calculating a confidence interval for the population proportion. The number of successes (22% of 6,000 = 1,320) and the number of failures (4,680) both exceed 15. The number of men between 50 and 64 in the country certainly exceeds 60,000 (10 times the sample size).

We can state with 95% confidence the proportion of men between 50 and 64 who participated in binge drinking within the last month is 22% plus or minus 1.0%. Put another way, the proportion of men between 50 and 64 who participated in binge drinking within the last month is between 21% and 23%.

Using the TI-83

1.96 0.22 0.78 6000 calculates the margin of error and stores it as M (you could use any variable but I chose M for margin of error).

0.22 calculates the lower bound of the interval by subtracting the margin of error.

0.22 calculates the upper bound of the interval by adding the margin of error.

Using Some Other Calculators

1.96 * ( 0.22 * 0.78 / 6000 ) sqrt=MS calculates the margin of error and stores it in memory.

0.22 - MR = calculates the lower bound of the interval by subtracting the margin of error from the sample proportion.

0.22 + MR = calculates the upper bound of the interval by adding the margin of error to the sample proportion.

 

Example 3

In the same study on binge drinking, only 6% of the 5,000 women who were 50 to 64 years old reported that they were binge drinkers. Find a 99% confidence interval for the proportion of women between 50 and 64 who are binge drinkers.

This sample clearly meets the requirements for calculating a confidence interval for the population proportion. The number of successes (6% of 5000 = 300) and the number of failures (4,700) both exceed 15. The number of women between 50 and 64 in the country certainly exceeds 50,000 (10 times the sample size).

The proportion of women between 50 and 64 who binge drink is 6% with a margin of error of 0.87% (that is, somewhere between 5.13% and 6.87%).

Using the TI-83

2.576 0.06 0.94 5000 calculates the margin of error and stores it as M (you could use any variable but I chose M for margin of error).

0.06 calculates the lower bound of the interval by subtracting the margin of error.

0.06 calculates the upper bound of the interval by adding the margin of error.

Using Some Other Calculators

2.576 * ( 0.06 * 0.94 / 5000 ) sqrt=MS calculates the margin of error and stores it in memory.

0.06 - MR = calculates the lower bound of the interval by subtracting the margin of error from the sample proportion.

0.06 + MR = calculates the upper bound of the interval by adding the margin of error to the sample proportion.