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DATA SHEET A

# DATA SHEET A - TABLES AND FORMULAS FOR MOORE Basic Practice...

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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- μ σ 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): ˆ y = a + bx with slope b = rs y /s x and intercept a = y- b x • Residuals: residual = observed y- predicted y = y- ˆ 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 μ and standard deviation σ / √ 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 ( σ known, SRS from Normal population): x ± z * σ √ n z * from N (0 , 1) • Sample size for desired margin of error m : n = z * σ m 2 • z test statistic for H : μ = μ ( σ known, SRS from Normal population): z = x- μ σ / √ 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 : μ = μ (SRS from Normal population): t = x- μ 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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DATA SHEET A - TABLES AND FORMULAS FOR MOORE Basic Practice...

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