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a sample in which the items have unknown probabilities of being selected. Example: Convenience Sample and judgement sampling 


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sample in which items are selected based upon known probabilities. Example: Simple Random Sample, systematic, stratified, and cluster 


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making conclusions about the population, that is, for statistical inference. 

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****Probability sampling is NECESSARY when 


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the error incurred by taking a sample instead of a census. (Remember as soon as you look at anything less than the entire population, you are not going to report with 100% accuracy the characteristics of the population). 


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(referred to as Bias) – error that results in a distortion of conclusions. 


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error incurred when some subjects refuse to respond to a survey
Example: Estimating percentage of car crashes that involve alcohol. Drunk drivers usually refuse the BAC test. 


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occurs when certain items are excluded from the sampling frame. 


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when data collected do not reflect the true measures.
Example: CDC Hepatitis Survey, Teacher Evaluation requiring you to fill in your name, order of survey questions, etc. 


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To make conclusions about the population based upon a single sample. 

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Major Goal of inferential statistics: 


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The sample proportion is used to estimate the actual proportion of the votes that each candidate will get from the population of voters (i.e: those people who actually get out and vote). 


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( ) as a random variable itself.Definition: The set of all possible sample statistics ( ’s) could be represented by a histogram, or distribution. This distribution is referred to as a sampling distribution. 


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mean and standard deviation. 

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The sampling distribution has its own 


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sampling distribution of the mean. 

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The distribution of all possible sample means is called the 


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If the population is not normal (or unknown), then the shape of the sampling distribution is normal for large samples (n≥30). 


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consists of a single sample statistic used to estimate the true value of the population parameter (either µ or π). 


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the parameter of interest is the population proportion of successes, π. 

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Remember that for categorical variables 


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items are selected based only on the fact that they are easy, inexpensive, or convenient to sample. 


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you get the opinions of preselected experts in the subject matter 


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Simple random sample and Systematic sample 

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Simple to use May not be a good representation of the population’s underlying characteristics 


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Ensures representation of individuals across the entire population 


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More cost effective Less efficient (need larger sample to acquire the same level of precision) 


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good questions elicit good responses 


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Coverage error or selection bias SE 

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Exists if some groups are excluded from the frame and have no chance of being selected 


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Non response error or bias SE 

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People who do not respond may be different from those who do respond 


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Variation from sample to sample will always exist 


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Due to weaknesses in question design, respondent error, and interviewer’s effects on the respondent (“Hawthorne effect”) 


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Standard Error of the Mean
Note that the standard error of the mean decreases as the sample size increases 

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A measure of the variability in the mean from sample to sample is given by the 


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Definition


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As the sample size gets large enoughthe sampling distribution of the sample mean becomes almost normal regardless of shape of population 


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single number, the sample statistic estimating the population parameter of interest 


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provides additional information about the variability of the estimate 


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provides more information about a population characteristic than does a point estimate 


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Point Estimate ± (Critical Value)(Standard Error) 

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The general formula for all confidence intervals is: 


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is the standard deviation of the point estimate 


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substitute the sample standard deviation, S 

Definition
If the population standard deviation σ is unknown, we can 


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adding an allowance for uncertainty to the sample proportion ( p ) 

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An interval estimate for the population proportion ( π ) can be calculated by 


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Sampling is less time consuming and less costly Sampling provides an objective way to calculate the sample size in advance Sampling provides results that are objective and defensible. Because the sample size is based on demonstrable statistical principles, the audit is defensible before one’s superiors and in a court of law
Sampling provides an estimate of the sampling error Allows auditors to generalize their findings to the population with a known sampling error. Can provide more accurate conclusions about the population Sampling is often more accurate for drawing conclusions about large populations. Examining every item in a large population is subject to significant nonsampling error Sampling allows auditors to combine, and then evaluate collectively, samples collected by different individuals. 

Definition
Six advantages of statistical sampling in auditing 

