Stats Durham College
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| Reason to Sample | The results of a sample may adequately estimate the value of the population parameter, thus saving time and money
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| Reason to Sample | It may be too time consuming to contact all members of the population
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| Reason to Sample | It may be impossible to check or locate all the members of the population
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| Reason to Sample | The cost of studying all the items in the population may be prohibitive
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| Reason to Sample | Often, testing destroys the sampled item and it cannot be returned to the population
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| Simple Random Sample | A sample selected so that each item or person in the population has the same chance of being included
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| Systematic Random Sampling | A random starting point is selected, and then every kth member of the population is selected
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| Stratified Random Sampling | A population is divided into subgroups, called strata, and a sample is randomly selected from each stratum
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| Cluster Sampling | A population is divided into clusters using naturally occurring geographic or other boundaries. Then, clusters are randomly selected and a sample is collected by randomly selecting from each cluster
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| Sampling Error | The difference between a sample statistic and its corresponding population parameter
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| Sampling Distribution of the Sample Mean | A probability distribution of all possible sample means of a given sample size
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| Central Limit Theorem | If all samples of a particular size are selected from any population, the sampling distribution of the sample mean is approximately a normal distribution. This approximation improves with larger samples
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| Proportion | The fraction, ratio, or percent indicating the part of the sample or the population having a particular trait of interest
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| Sampling Distribution of the Sampling Proportion | A probability distribution of all possible sample proportions of a given sample size
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| Sampling Distribution of the Sample Mean | For a given sample size, the mean of all possible sample means selected from a population is equal to the population mean
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| Sampling Distribution of the Sample Mean | There is less variation in the distribution of the sample mean than in the population distribution
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| Sampling Distribution of the Sample Mean | The standard error of the mean measures the variation in the sampling distribution of the sample mean. The sample error is found by:
stdev(sub x-bar)=stdev/sqrt(n)
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| Sampling Distribution of the Sample Mean | If the population follows a normal distribution, the sampling distribution of the sample mean will also follow a normal distribution for samples of any size
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| Sampling Distribution of the Sample Mean | Assume the population standard deviation is known. To determine the probability that a sample mean falls in a particular region, use the following formula:
z=x-bar - mu/(stdev/sqrt(n))
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| Sampling Distribution of the Sample Mean | The sampling distribution of the proportion follows a normal distribution if np and n(1-p) >5.
1. The sample proportion is p-bar=x/n
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| To determine the probability that a sample proportion falls in a particular region, use the following formula: | z=p-bar-p/(sqrt(p(1-p))/n)
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| mu sub x bar | mean of the sampling distribution of the sample mean
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| sigma sub x bar | population standard error of the sample mean
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| s sub x bar | estimate of the standard error of the sample mean
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| sigma sub p bar | population standard error of the sample proportion
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