Which two of the following conditions must be met in order to infer statistical significance about the results of an audit sample? I. The population must be homogeneous. II. The sample size must be greater than 10. III. The sample must be random. IV. The sample must be taken from multiple locations.

For the results of an audit sample to be used for statistical inference about the entire population, two fundamental conditions must be met. First, the sample must be selected randomly (III). Randomness ensures that every item in the population has an equal and independent chance of being selected, which minimizes bias and allows the laws of probability to be applied. Second, the population from which the sample is drawn must be homogeneous (I). This means all items in the population share similar characteristics. If the population is not homogeneous, any random sample may not be representative, and inferences would be invalid. In such cases, the population must first be divided into homogeneous subgroups (stratification) before random sampling is performed within each subgroup.

A. I and II: The condition that the sample size must be greater than 10 (II) is an arbitrary rule of thumb, not a fundamental requirement for statistical significance.
C. II and III: While randomness (III) is essential, the sample size requirement of being greater than 10 (II) is not a universal prerequisite for making statistical inferences.
D. III and IV: Sampling from multiple locations (IV) is a practical technique to ensure representativeness in a geographically dispersed population, but it is not a core statistical necessity for all audits.

1. Russell, J. P. (Ed.). (2021). The ASQ Certified Quality Auditor Handbook (5th ed.). ASQ Quality Press. In Chapter 18, "Audit Sampling," the text emphasizes that "For a sample to be statistical, it must be randomly selected" (p. 298). The chapter also explains stratification as a method used when a population "is not homogeneous" to divide it into "homogeneous subgroups" before sampling (p. 301). This underscores that sampling is performed on homogeneous groups.

2. Montgomery, D. C. (2013). Introduction to Statistical Quality Control (7th ed.). John Wiley & Sons. Chapter 15, "Lot-by-Lot Acceptance Sampling," states, "A fundamental requirement of acceptance sampling is that the sample be selected at random... Random sampling is critical to the success of any sampling procedure" (p. 698). The concept of a "lot" inherently assumes a batch of product produced under uniform (homogeneous) conditions.

3. Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences (9th ed.). Cengage Learning. Chapter 1, Section 1.2, "Populations, Samples, and Processes," introduces the concept of a simple random sample, which is foundational to inference. The validity of many statistical procedures relies on the sample being drawn from a single, stable population distribution, which implies homogeneity.