ACCA Applied Knowledge · Management Accounting · Sampling methods
A population of 2,000 items has a known mean of 50. A researcher draws a random sample of 100 items and finds a sample mean of 52.4. Which statement is correct?
The 2.4 difference is sampling error, the gap between the sample mean of 52.4 and the population mean of 50 caused by examining only part of the population. Random selection does not guarantee the sample mean equals the population mean, and the difference alone does not indicate a faulty frame.
- AThe difference of 2.4 is sampling error, arising because only part of the population was examinedCorrect
- BThe difference of 2.4 shows the sampling frame was wrong
- CThe difference of 2.4 is non-sampling error and can only be removed by enlarging the sample
- DThe sample mean must be 50 if selection was random
Explanation
Sampling error is the difference between a sample statistic and the true population parameter due to observing only part of the population. Here it is 52.4 - 50 = 2.4. Random selection does not guarantee equality, and a difference alone does not prove a frame fault or non-sampling error.
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