Question

To find the percent error when comparing Bob's estimate to the actual attendance at the concert, you can use the following formula:

Percent Error = | (Estimated Value−Actual Value)/(Actual Value)| ×100
In this case:
The estimated value is 230 people.
The actual value is 300 people.

Answer 1

The percent error of Bob's estimate is approximately 23.33%. The ±3 percent represents the maximum sampling error, with an increased sample size being a method to lower this error.

Step-by-step explanation:

To calculate the percent error when comparing Bob's estimate to the actual attendance at the concert, you would follow the formula provided: Percent Error = | (Estimated Value − Actual Value) / (Actual Value)| × 100. Using the given estimated value of 230 people and the actual value of 300 people, the calculation would be as follows:

Percent Error = | (230 − 300) / 300| × 100
Percent Error = | (-70) / 300| × 100
Percent Error = | -0.2333... | × 100
Percent Error = 0.2333... × 100
Percent Error = 23.33...

Therefore, the percent error of Bob's estimate is approximately 23.33%.

Regarding the concept of sampling error, the ±3 percent error bound mentioned refers to the maximum sampling error that the researchers are willing to accept. This signifies an estimate that 95% of the time, the true value will be within 3 percentage points of the estimated percentage. To lower the sampling error, increasing the sample size is one effective method.