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30 Cards in this Set
- Front
- Back
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Describe estimation
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prediction of confidence intervals for parameters
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Describe significance testing
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judging whether sample evidence is consistent with a hypothesis
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Describe the Poisson distribution
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Discrete distribution
Shape - right-skewed to almost symmetrical Describes the occurence of 'isolated events within a continuum' Similar to binomial, but with infinite sample size |
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How is Poisson like binomial
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Binomial - based on taking samples from a population who elements are of two types
Poisson - takes a sample from a population of elements of two types (split into events and the non-occurence of events |
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Applications of Poisson distribution
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1. Arrival of telephone calls
2. Flaws in telegraph cable 3. Mechanical breakdown of machinery 4. Clerical errors |
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The Poisson distribution is derived from ...
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the binomial.
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What is key assumption for Poisson distribution?
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Sample is taken at random.
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What are the two tests to check whether the Poisson is applicable?
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1. Actual situation is compared qualitatively with that on which the distribution is based
2. Some observed data are compared with what is theoretically expected. |
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When can the Poisson approximate the binomial?
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When the sample is large and the proportion is small. n > 20 and p < 0.05
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Define Degrees of Freedom
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The number of observations that are free to vary in estimating a parameter from a sample.
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Describe the significance of the Degrees of Freedom
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the degrees of freedom associated with the estimate of a parameter is the sample size minus the number of observations used up because of the need to measure other statistics (exception - mean - equals sample) e.g. for standard deviation, the degrees of freedom are n - 1. In other cases, may be more than 1.
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Describe t-Distribution
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the t-distribution overcomes the the sample size restriction of the standard distribution, thereby allows small sample work to be done.
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Characteristics of t-distribution
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Continuous
Long tails Similar to normal distribution Shape is symmetrical For sample sizes of >30, t-dist and normal coincide (to good approx). |
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Situations where t-distributions occur.
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Used in place of the sampling distribution of mean:
a. Population standard deviation is not known and has to be estimated b. Sample size less than 30 c. Underlying distribution taken to be normal |
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What is the t-distribution also known as?
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Student's t-Distribution
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The 5 stages of significance test for t-distributions is?
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a. Specify the hypothesis
b. Collect sample evidence c. Set the Significance level d. Calculate t value related to sample evidence e. Compare the observed t value with the t value associated with the significance level. Accept or reject hypothesis accordingly. |
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What are the parameters for the t-distribution?
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a. arithmetic mean
b. standard deviation c. degrees of freedom |
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How to decide whether data has a t-distribution.
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The individual distribution must be normal. Can be checked by taking small sample and observing distribution
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What are the four major distributions?
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1. Binomial
2. Normal 3. Poisson 4. t |
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Describe the chi-squared distribution.
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provides the method for comparing an observed sample variance with a hypothesized population variance.
Answers question: Is the observed scatter of the sample in accord with what is thought to be the scatter of the population? |
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Describe the shape of the chi-squared distribution
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Shape can vary depending on the degrees of freedom. As it approaches 30, the distribution becomes more like a normal distribution.
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Important assumptions for the chi-squared distribution
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1. Sample must be taken from random from a normal population, or if not normal, then
2. Sample size is > 30. |
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Estimation for chi-squared distribution is based on ...
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finding confidence limits for chi-squared and then transforming these into variances.
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What is one of the most common managerial uses of the chi-squared distribution
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test for differences in proportions
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Describe the F-Distribution
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used to compare the variance of one sample with that of a second.
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How are degrees of freedom counted in the F-Distribution?
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one for the sample variance in numerator; one for the sample variance in the denominator. Each of these is sample size minus one.
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What is the major application of the F-Distribution?
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in the analysis of variance.
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What are the two important assumptions related to the F-Distribution.
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1. Samples must be selected at random.
2. the population form which the samples came should be normally distributed. |
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Describe the Negative Binomial distribution
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applicable to situations that almost fit the Poisson.
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Describe the Beta-binomial distribution
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Applicable in situations where the binomial is not quite sufficient.
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