Question

Compare the actual errors with the error estimates found by using the smallest possible values of k.

a. Actual errors are always smaller than error estimates.
b. Actual errors are always larger than error estimates.
c. Actual errors may be smaller or larger than error estimates.
d. Actual errors are unrelated to error estimates.

Answer 1

The correct answer is c. Actual errors may be smaller or larger than error estimates. Error estimates are calculated to be safe margins, but actual errors can vary and may not always align perfectly with these estimates.

Step-by-step explanation:

When comparing actual errors and error estimates, c. Actual errors may be smaller or larger than error estimates is the correct choice. In statistical sampling, an error estimate is calculated to give an idea of how far the sample statistic is likely to be from the population parameter. This involves an estimation of the sampling error which is affected by sample size and variability within the population.

Error estimates are designed to be conservative to provide a margin of safety, often based on the smallest possible value of the error bounds (k). However, the actual error, which is the difference between the sample statistic and the true population parameter, could turn out to be either smaller or larger than this estimate. As the sample size increases, the error bound generally decreases, thus improving the estimate's accuracy.

Note that there is always uncertainty in numbers taken from graphs or data sets, and it is important to assess these values within the context of the estimated uncertainties to determine their reliability.