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Unformatted text preview: Definition and Terms Definition and Terms
• Statistics: the science of collecting, analyzing, interpreting, and presenting data • Terms:
– – – – Descriptive vs. Inferential Population (census, parameters) Sample (survey, statistics) Scales: nominal, ordinal, interval, ratio Descriptive Statistics Descriptive Statistics
• Visual presentations:
– Frequency distributions, graphs – Mean, median, mode, • Measures of central tendency: • Measures of dispersion: • Measures of shape:
– Skewness, kurtosis, – Range, variance, standard deviation Probability Probability
• Numerical measure of the likelihood that an • •
event will occur Scale from 0 – 1 Probability function, f(x)
– – Discrete – probability that x assumes a specific value Continuous – probability that x assumes a value in a given interval Continuous Probability Distributions Continuous Probability Distributions
• Normal distribution
– Two parameters, mean & standard deviation – symmetrical x Sampling distributions Sampling distributions
• Sample mean xbar is a random variable Sample xbar
– – – Mean or expected value Standard deviation Probability distribution • Sampling distribution of xbar Sampling xbar E( x ) = µ σ σx = n Confidence Intervals Confidence Intervals
• Interval Estimation:
– Range of values, containing parameter (with some degree of confidence) – Point estimate + margin of error x ± zα / 2 σ n x ± tα / 2, n −1 s n Hypothesis Testing Hypothesis Testing • Determine whether a statement about the value • • •
of a parameter should be rejected. Null hypothesis Alternative hypothesis Sigma known or unknown Tests Involving a Population Mean Tests Involving a Population Mean
The equality part of the hypotheses always appears in the null hypothesis. H 0 : µ ≥ µ0 H a : µ < µ0
Onetailed (lowertail) H 0 : µ ≤ µ0 H a : µ > µ0
Onetailed (uppertail) H 0 : µ = µ0 H a : µ ≠ µ0
Twotailed Decision Rules Decision Rules Interval Estimation of Mean1 – Mean2 Interval • • • Sigma known Point estimate = xbar1 – xbar2 Point estimate + margin of error ( x1 − x2 ) ± zα 2 σσ + n1 n2
2 1 2 2 Hypothesis Tests: Mean1 – Mean2 Hypothesis Tests: Mean
• • •
Level of significance Compute test statistic Find pvalue ( x1 − x2 ) −( µ1 − µ2 ) z=
σ12
n1 +
2 σ2 n2 ...
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This note was uploaded on 01/13/2011 for the course MS 3043 taught by Professor Dell during the Spring '09 term at The University of Texas at San Antonio San Antonio.
 Spring '09
 DELL

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