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# 1023 Review - Definition and Terms Definition and Terms •...

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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 x-bar is a random variable Sample x-bar – – – Mean or expected value Standard deviation Probability distribution • Sampling distribution of x-bar Sampling x-bar 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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