Final answer:
The likely margin of error in a client's test score is best represented by the Standard Error of Measurement, which is used along with the confidence level to calculate the margin of error within a confidence interval.
Step-by-step explanation:
In this context, the measure that tells you the likely margin of error in your client's test score is c) the Standard Error of Measurement. The standard error of measurement provides an estimate of the variability of scores due to measurement error, which is essential when interpreting individual test scores and their precision. The margin of error is particularly important for creating confidence intervals, which are ranges centered around a sample statistic (like a mean) that likely contain the population parameter being estimated.
When constructing a confidence interval, statisticians use the formula of the point estimate ± the margin of error. The margin of error depends on the desired confidence level and the standard error of the mean. The standard error itself reflects the sampling variability and is the standard deviation of the sampling distribution, representing the average amount that the sample mean would differ from the population mean if different samples were taken.
It is also worth noting that when sample sizes are small, usual estimations of the population standard deviation using the sample standard deviation can lead to inaccuracies; hence, in such cases, alternative approaches or adjustments may be necessary for reliable inference.