An auditor randomly samples 20 accounts receivable from...

An auditor randomly samples 20 accounts receivable from among the 500 such accounts of a client's firm. The auditor lists the amount of each account and checks to see if the underlying documents comply with stated procedures. The data are recorded in the accompanying table (amounts are in dollars, $Y=$ yes, and $N=n o$ ). Estimate the total accounts receivable for the 500 accounts of the firm and place a bound on the error of estimation. Do you think that the average account receivable for the firm exceeds $\$ 250 ?$ Why?

An auditor randomly samples 20 accounts receivable from among the 500 such accounts of a client's firm. The auditor lists the amount of each account and checks to see if the underlying documents comply with stated procedures. The data are recorded in the accompanying table (amounts are in dollars, $Y=$ yes, and $N=n o$ ).
Estimate the total accounts receivable for the 500 accounts of the firm and place a bound on the error of estimation. Do you think that the average account receivable for the firm exceeds $\$ 250 ?$ Why?

Key Concepts

Simple Random Sampling

This concept involves selecting a subset of individuals or items from a larger population such that every member of the population has an equal probability of being chosen. In the context of auditing accounts receivable, using a simple random sample helps ensure that the estimated total or average is representative of the entire group, reducing potential bias in the estimation process.

Estimation of Population Totals

Estimating a population total involves scaling up the statistics obtained from a sample to the entire population. In this case, the auditor uses the average amount from the sample and multiplies it by the total number of accounts to estimate the overall accounts receivable. This method relies on the assumption that the sample is representative of the population.

Standard Error and Margin of Error

The standard error measures the variability of the sample statistic from the true population parameter. It is crucial for understanding the precision of the estimate. The margin of error, which is often derived from the standard error and a chosen confidence level, provides a bound within which the true value of the total or average is likely to lie, indicating the reliability of the estimation.

Confidence Interval Estimation

This concept involves constructing an interval around the sample estimate that is likely to contain the true population parameter with a specified level of confidence (for example, 95%). In this scenario, a confidence interval would be used to place bounds on the estimated total accounts receivable and to assess whether the average account receivable likely exceeds the $250 threshold.

Hypothesis Testing for the Mean

Hypothesis testing assesses whether the sample data provide enough evidence to reject a null hypothesis about the population mean. In the context of this question, testing whether the average account receivable exceeds $250 involves comparing the sample estimate and its confidence interval against this threshold, ultimately helping determine if there is sufficient statistical support for the claim.

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