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There are six key aspects in variables sampling. I'd like to present the first three parts and
the other will be covered by Pham Huong.
Like monetary unit sampling, variables sampling is a statistical sampling method (also
known by a different name as estimation sampling). Now remember that when we talk
about variables sampling we’re looking dollar amount, the reasonableness of client
number to determine whether accept or reject client balance.
You have to understand that this method uses standard deviation. It’s the distribution of
number around the mean. I will explain more briefly in couple minutes.
Variable and Nonstatistical Sampling share many similarities:
+ Objective: to measure the misstatement in an account balance.
+ All 14 steps we discussed for nonstatistical sampling must be performed for
variable methods. (Move)
Now bear in mind that The auditor doesn’t know the mean value of misstatements in the
population, why? Because they’re only sampling. They also don’t know also the
distribution of population or the audited value. So, they’re gonna use techniques to
estimate the population characteristics from sample. Three methods are often used:
difference estimation, ratio estimation and mean per unit estimation which will be
discussed by Pham Huong later.
Now, I can say that It is useful to understand sampling distributions and how they affect
auditors’ statistical conclusions of population.
$36 ± $12 at a 99.7% confidence level (move)
Here is an example about the confidence interval of the population mean gained from the
study of sample distribution. It refers that we are ninety nine point seven percent
confident that the sample mean is within thi dollars to forty eight dollars. And assume
that our population is one hundred account receivables, we can estimate that the total
population misstatement is between twenty four thousand dollar and forty eight thousand
dollar.
Now, I will show you how to find out the interval.
(SLIDE) The first thing that has to compute is the mean of sample by the function
After calculating the mean for each sample, we plot them into a frequency distribution
Here, I have an assumption that the sample size is large enough that it represents a
normal distribution curve.
(SLIDE) And you have to remember that The mean value of all the samples is equal to
the population mean. We have learned about it in Statistical class. (move)
Back to the our lesson The distribution of the sample means has all the
characteristics of the normal curve: Which are The curve is symmetrical and The
sample means fall within known portions of the value of sampling distribution
around the average mean of those means, measured by standard deviation(move).
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Standard deviation is the measure of how much sample distributions vary from the mean.
The more they vary from the mean, the riskier the population is.
So we’re saying here we can easily compute the standard deviation of sampling
distribution which is called the standard error (SE): by the function on the screen
SE = SD/sqrt(n)
(This is again some statistical background. We have one standard deviation with sixty
eight point two percent confidence, two standard deviations with ninety five point four
percent confidence and three standard deviations with ninety nine point seven percent.
We can take these figure from the normal distribution table. Let’s move to an example to
understand more briefly. (move)
Example
Assume a population with a mean of forty dollar and a standard deviation of fifteen
dollar, from which we elected to take many random samples of one hundred items each.
The standard error of our sampling distribution is equal to fifteen dollar divided by square
root of one hundred, equal to one point five dollar
This is the tabulation of this sampling distribution.
Within one standard error we have sixty eight point two percent confidence and then we
take one standard error times one point five which is value of standard error. We can say
we are sixty eight point two percent confident that the average of population is within
thirsty eight point five and forty one point five. With two and three SE we do the same
way. (move)
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The example we have just implemented illustrates statistical reference which is a
conclusion that the auditor draw from sample results based on the knowledge of
sampling distributions. (move)
(SLIDE) You can see on the screen or your textbook the general format of a confidence
level of the population mean. (back slide)
Auditors can state the conclusions drawn from a confidence interval using statistical
inferences by upper and lower confidence limits or different ways that you can read
by yourself in your textbook as long as taking care to avoid incorrect conclusions because
the true population value is always unknown.
Pham Huong will continue our presentation about variables methods.