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20 Cards in this Set
- Front
- Back
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What are the 3 criteria for Random Samples?
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1. Equal Chance
2. The selection of any single case or unit cannot affect the selection of any other unit or case. 3. The cases or units should be selected in such a way that all combinations are possible. |
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Sampling Error?
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The difference between a sample statistic and population parameter that is just due to chance.
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Sampling Frame?
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Physical representation of the population.
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Sampling Distribution?
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Simply means a distribution that is the result of repeated sampling.
Tells you how a statistic behaves. |
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Central Limit Theorem?
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If repeated random samples of size (n) are taken from a population with a means or mu and a standard deviation (sigma), the sampling distribution of sample means will have a mean equal to mu and a standard error equal to (sigma over the square root of n). Moreover, as (n) increases, the sampling distribution will approach a normal distribution.
CI = (X with line above - mean) + or - t or z times (s with smaller x and line - mean) |
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Sigma Known?
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Calculate the standard error of the mean.
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Sigma Unknown?
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Estimate the standard error of the mean.
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Confidence Interval for the mean?
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An interval or range of values within which the true mean of the population is believed to be located.
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Confidence Interval Formula?
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CI = mean (+ or -) z or t (times standard error)
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What is the Z value at a 95% confidence interval?
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1.96
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What is the Z value at a 99% confidence interval?
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2.58
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According to the Central Limit Theory, what is the relationship between the standard deviation of the population (sigma) and the standard error?
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The standard error is equal to sigma divided by the square root of the sample size.
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How is the standard error calculated when the standard deviation of the population (sigma) is known?
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The standard deviation of the population (sigma) is divided by the square root of the sample size.
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What is the relationship between the level of confidence and the precision of an estimate when constructing a confidence interval for the mean?
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Level of confidence and precision are inversely related. As one increases, the other decreases.
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What effect does increasing the size of a sample have on the width of the confidence interval and the precision of the estimate?
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It decreases the width of the interval and increases the precision of the estimate.
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When using the t table and constructing a confidence interval for the mean (with sigma unknown), how is the number of degrees of freedom computed?
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The number of degrees of freedom will be equal to n-1.
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When using the t table (with sigma unknown), how do you find the level of confidence in the table?
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The level of confidence is expressed indirectly. It is equal to 1 - the level of significance.
For example: To work at the 95% level of confidence, use the column dedicated to the .05 level of significance (1 - .05 = .95) |
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What is the purpose behind the construction of a confidence interval for a proportion?
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A confidence interval for a proportion is constructed in an effort to estimate the proportion in a population, based upon a proportion in a sample.
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In a confidence interval for a proportion, what is the margin of error?
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The margin of error is an indirect statement of the width of the interval.
For example: The statement that the proportion in a population is estimated at 45% with a margin of error (+ or -)3% is actually a statement that the interval of the estimate ranges from 42% to 48% |
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Given a constant level of confidence, what is the effect on the margin of error of increasing the sample size when developing a confidence interval for a proportion?
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Given a constant level of confidence, an increase in the size of a sample will decrease the margin of error.
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