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sampling involves
selecting representative items from a population, examining those selected items and drawing a conclusion about the population based on the results derived from the examination of the selected items
sampling allows auditors to draw conclusions about
populations that are too numerous for every item to be tested
statistics in sampling
auditors can test relatively small samples that allow them to draw conclusions about a population with measurable reliability
main issue in sampling is
choosing a sample that is representative of the population. valid conclusions may be stated about the population
for audit purposes, each item in a population is associated with
a variable of interest for the auditor
variables of interest can be either
discrete variables or continuous variables
discrete variables
such as yes/no decision whether to authorize payments of invoices, tested using attribute sampling
continuous variables
such as monetary amounts of accounts receivable, tested using variables sampling
an important characteristic of a population is
the distribution of the values of the variable of interest
what is the most important distribution of values of a variable of interest
normal distribution - bell curve. values form a symmetrical bell shaped curve centered around the mean
shape, height and width of a population's distribution curve are quantified through
its measures of central tendency
mean
arithmetic average of a set of numbers
median
middle value if data are arranged in numerical order. half the values are smaller than the median and half are larger. it is the 50th percentile
mode
most frequently occurring value. if all values are unique, no mode exists
in a normal distribution, how are mean, median and mode?
the same, and tails are identical
if mean is greater than mode
it is an asymmetrical frequency distribution. the right tail is longer and the distribution is positively skewed to the right
accounting distributions tend to be skewed
to the right. accounts receivable generally include many medium and low value items and few high value items
if median is greater than the mean
left tail is longer and the distribution is negatively skewed to the left
best estimate of central tendency for many asymmetrical distributions
median, because median is not biased by extremes
a population's variability is the extent to which the values of items are
spread about the mean - dispersion.
population variability is measured by
standard deviation
standard deviation is
measure of the dispersion of a set of data from its mean
if item has little dispersion, standard deviation is
small
if the item is highly dispersed, bell curve is? standard deviation is?
bell curve is relatively flat and standard deviation is large
1 standard deviation in a normal distribution
68%
1.64 standard deviation in a normal distribution
90%
1.96 standard deviation in a normal distribution
95%
2 standard deviation in a normal distribution
95.50%
3 standard deviation in a normal distribution
99%
2.57 standard deviation in a normal distribution
99.70%
confidence level is
percentage of times/ probability that a sample is representative of the population. desired reliability of the sample. the greater the desired confidentiality level, the bigger the sample size should be ex: confidence level of 95% should result in representative samples 95% of the time
confidence interval for a given confidence level is
the range around a sample value that is expected to contain the true population value. confidence interval may also be referred to as precision
how is confidence interval constructed
using the confidence coefficient for the number of standard deviations for the confidence level chosen.
if confidence interval is 6% of a random sample, and 88% of sample has a characteristic, what is the confidence that the population has the characteristic?
between 82% and 94%
for a given confidence level, size of the confidence interval depends on
the sample size.
if sample size changes, how does that affect confidence interval
increased sample size decreases the confidence interval, meaning that the true population value is expected to be in the narrower range around the sample value
after sample is set, how can the confidence interval change?
confidence level. if confidence level increases, then the confidence interval will widen. if confidence level is decreased, then the confidence interval will be narrowed
how can we estimate the standard deviation of a population?
use a pilot sample
what is the standard error of the mean
standard deviation of the distribution of sample means. standard error is used to compute precision. the larger the standard error, the wider the interval
what is the coefficient of variability
measures the relative variability within the data and is calculated by dividing standard deviation of the sample by the mean.
variability of a population, as measured by standard deviation, is
extent to which the individual values of the items in the population are spread about the mean
population is
in a sampling application, the group of items about which the auditor wants to estimate some characteristic
judgmental sampling
uses the auditor's subjective judgment to determine the sample size and sample selection
what is the advantage of judgmental sampling
subjectivity is not always a weakness. auditor can select and test only items considered to be important.
disadvantage of judgmental sampling
does not provide quantitative measure of sampling risk, does not provide quantitative expression of sample results, and if auditor is not proficient, sample may not be effective
define statistical sampling
provides an objective method of determining sample size and selecting items to be examined.
pros of statistical sampling
quantitative measure of sampling risk, confidence level, and precision. quantitative expression of sample results. helps auditor to design an efficient sample
cons of statistical sampling
can be more expensive and time consuming than nonstatistical sampling. requires special statistical knowledge and training. requires statistical software.
nonsampling risk
audit risk not related to sampling. common audit risk is auditors failure to detect an error in a sample.
causes of nondetection of an error in sample
auditor inattention or fatigue. can be caused by application of inappropriate audit procedure, such as looking for the wrong approvals in a sample of documents
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