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Unformatted text preview: TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics Exploring Data: Distributions Look for overall pattern (shape, center, spread) and deviations (outliers). Mean (use a calculator): x = x 1 + x 2 + + x n n = 1 n x i Standard deviation (use a calculator): s = 1 n- 1 ( x i- x ) 2 Median: Arrange all observations from smallest to largest. The median M is located ( n + 1) / 2 observations from the beginning of this list. Quartiles: The first quartile Q 1 is the median of the observations whose position in the ordered list is to the left of the location of the overall median. The third quartile Q 3 is the median of the observations to the right of the location of the overall median. Five-number summary: Minimum , Q 1 , M, Q 3 , Maximum Standardized value of x : z = x- Exploring Data: Relationships Look for overall pattern (form, direction, strength) and deviations (outliers, influential observations). Correlation (use a calculator): r = 1 n- 1 x i- x s x y i- y s y Least-squares regression line (use a calculator): y = a + bx with slope b = rs y /s x and intercept a = y- b x Residuals: residual = observed y- predicted y = y- y Producing Data Simple random sample: Choose an SRS by giving every individual in the population a numerical label and using Table B of random digits to choose the sample. Randomized comparative experiments: Random Allocation Group 1 Group 2 Treatment 1 Treatment 2 Observe Response Probability and Sampling Distributions Probability rules: Any probability satisfies 0 P ( A ) 1. The sample space S has probability P ( S ) = 1. If events A and B are disjoint, P ( A or B ) = P ( A ) + P ( B ). For any event A , P ( A does not occur) = 1- P ( A ) Sampling distribution of a sample mean: x has mean and standard deviation / n . x has a Normal distribution if the popula- tion distribution is Normal. Central limit theorem: x is approximately Normal when n is large. Basics of Inference z confidence interval for a population mean ( known, SRS from Normal population): x z * n z * from N (0 , 1) Sample size for desired margin of error m : n = z * m 2 z test statistic for H : = ( known, SRS from Normal population): z = x- / n P-values from N (0 , 1) Inference About Means t confidence interval for a population mean (SRS from Normal population): x t * s n t * from t ( n- 1) t test statistic for H : = (SRS from Normal population): t = x- s/ n P-values from t ( n- 1) Matched pairs: To compare the responses to the two treatments, apply the one-sample t proce- dures to the observed di ff erences....
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