4. Selecting the sampling Approach
a. In a random sample, every item in the population has an equal and nonzero chance of being selected.
1) If enough large random samples are drawn, the mean of their means will approximate the population mean closely enough that they are considered to be representative of the population.
2) For very large populations, the absolute size of the sample affects the precision of its results more than its size relative to the population. Thus, above a population a certain population size, the sample size generally does not increase.
3) The traditional means of ensuring randomness is to assign a random number to each item in the population. Random number tables are often used for this purpose.
a) Random number tables contain collections of digits grouped randomly into columns and clusters. After assigning numbers to the members of the population, the tables can be used to select the sample items.
b. An interval (systematic) sampling plan assumes that items are arranged randomly in the population. If they are not, a random selection method should be used.
1) Interval sampling divides the population by the sample size and selects every nth item after a random start in the first interval. For example, if the population has 1,000 items and the sample size is 35, every 28th item (1,000/ 35= 28.57) is selected.
a) Interval sampling is appropriate when, for instance, an auditor wants to test whether controls were operating throughout an entire year. (A random sample might result in all items being selected from single month.)
b) Because interval sampling requires only counting in the population, no correspondence between random numbers and the items in the population is necessary as in random number sampling.