Tables and Formulas for Sullivan, Statistics: Informed Decisions Using Data<\/p>\n
Chapter 2: Organizing and Summarizing Data<\/p>\n
Relative frequency = frequencysum of all frequenciesClass midpoint: The sum of consecutive lower class limits divided by 2.<\/p>\n
Chapter 3: Numerically Summarizing Data<\/p>\n
Population Mean: \u03bc= \u03a3xiNSample Mean: x = \u03a3xinRange = Largest Data Value \u2013 Smallest Data Value<\/p>\n
Population Standard Deviation: \u03c3 = \u03a3(xi- \u03bc)2NSample Standard Deviation: s = \u03a3(xi- x)2n-1Population Variance: \u03c32Sample Variance: s2<\/p>\n
Empirical Rule: If the shape of the distribution is bell-shaped, then<\/p>\n
Approximately 68% of the data will lie within 1 standard deviation of the mean<\/p>\n
Approximately 95% of the data will lie within 2 standard deviations of the mean<\/p>\n
Approximately 99.7% of the data will lie within 3 standard deviations of the mean<\/p>\n
Population z-score: z = x- \u03bc\u03c3Sample z-score: z = x- xsInterquartile Range: IQR = Q3 – Q1Lower Fences = Q1-1.5(IQR) <\/p>\n
Upper Fence = Q3+1.5(IQR)Five-Number Summary<\/p>\n
Minimum, Q1, M, Q3, MaximumChapter 4: Describing the Relation between Two Variables<\/p>\n
Correlation Coefficient: -1 \u2264 r \u2264 1<\/p>\n
The equation of the least-squares regression line is y = b1x +b0, <\/p>\n
where y is the predicted value, b1 is the slope, and b0 is the y-intercept. <\/p>\n
Residual = observed y \u2013 predicted y<\/p>\n
= y – yThe coefficient of determination, R2, measures the proportion of total variation in the response variable that is explained by the least-squares regression line.<\/p>\n
Chapter 5: Probability<\/p>\n
Empirical Probability<\/p>\n
P(E) = frequency of Enumber of trials of experimentClassical Probability<\/p>\n
P(E) = number of ways that E can occurnumber of possible outcomes = N(E)N(S)Addition Rule for Disjoint Events<\/p>\n
P(E or F) = P(E) + P(F)<\/p>\n
General Addition Rule<\/p>\n
P(E or F) = P(E) + P(F) \u2013 P(E and F)<\/p>\n
Compliment Rule<\/p>\n
P(EC) = 1\u2013 P(E)<\/p>\n
Multiplication Rule for Independent Events<\/p>\n
P(E and F) = P(E)\u22c5P(F)<\/p>\n
Conditional Probability Rule<\/p>\n
P (F|E) = P(E and F)P(E)= N(E and F)N(E)General Multiplication Rule<\/p>\n
P (E and F) = P(E) \u22c5 P(F|E)<\/p>\n
Chapter 6: Discrete Probability Distributions<\/p>\n
Mean (Expected Value) of a Discrete Random Variable<\/p>\n
\u03bcX = \u03a3x \u22c5 P(x)<\/p>\n
Standard Deviation of a Discrete Random Variable<\/p>\n
\u03c3X = \u03a3 (x- \u03bc)2 \u22c5P(x)<\/p>\n
Binomial Probability Distribution Function<\/p>\n
13970002032000P(x) = n C x px(1-p)n-xMean and Standard Deviation of a Binomial Random Variable<\/p>\n
\u03bcX=np\u03c3X = np(1-p)<\/p>\n
Chapter 7: The Normal Distribution <\/p>\n
Standardizing a Normal Random Variable<\/p>\n
z = x – \u03bc\u03c3 <\/p>\n
Finding the Score: x = \u03bc+z\u03c3Chapter 8: Sampling Distributions<\/p>\n
Mean and Standard Deviation of the Sampling Distribution of x\u03bcx = \u03bc and\u03c3x = \u03c3nSample Proportion: p = xnMean and Standard Deviation of the Sampling Distribution of p\u03bcp = p and \u03c3p = p(1-p)nChapter 9: Estimating the Value of a Parameter<\/p>\n
Confidence Intervals<\/p>\n
A (1 \u2013 \u03b1)\u22c5100% confidence interval about p is p \u00b1 z\u03b1\/2\u22c5p(1 – p)nA (1 \u2013 \u03b1) \u22c5100% confidence interval about \u03bc is x \u00b1 t\u03b1\/2\u22c5snNote: t\u03b1\/2 is computed using n \u2013 1 degrees of freedom.<\/p>\n
Sample Size<\/p>\n
To estimate the population proportion with a margin of error E at a (1 \u2013 \u03b1)\u22c5 100% level of confidence:<\/p>\n
n = p (1 \u2013 p) z\u03b1\/2\u03952 rounded up to the next integer, where p is a prior estimate of the population proportion, or n = 0.25 z\u03b1\/2\u03952rounded up to the next integer when no prior estimate of p is available.<\/p>\n
To estimate the population mean with a margin of error E at a (1 \u2013 \u03b1) \u22c5 100% level of confidence: <\/p>\n
n = z\u03b1\/2\u22c5 s\u03952 rounded up to the next integer.<\/p>\n
Chapter 10: Hypothesis Tests Regarding a Parameter<\/p>\n
Test Statistics<\/p>\n
z0 = p- p0p0 (1- p0)nt0= x – \u03bc0 snChapter 11: Inferences on Two Samples <\/p>\n
Test Statistic Comparing Two Population Proportions (Independent Samples)<\/p>\n
z0 = p1- p2-(p1- p2)\u03c3(p1-p2) where p = x1+ x2n1+ n2Confidence Interval for the Difference of Two Proportions (Independent Samples)<\/p>\n
(p1- p2) \u00b1 z\u03b1\/2 \u22c5 \u03c3p1- p2Test Statistic for Matched-Pairs Data<\/p>\n
t0= d- \u03bcdsdnwhere d is the mean and sd is the standard deviation of the differenced data.<\/p>\n
Confidence Interval for Matched-Pairs Data<\/p>\n
d \u00b1 t\u03b12 \u22c5 sdnNote: t\u03b12 is found using n-1 degrees of freedom.<\/p>\n
Test Statistic Comparing Two Means (Independent Sampling)<\/p>\n
t0 = x1-x2-(\u03bc1-\u03bc2)s12n1+ s22n2Confidence Interval for the Difference of Two Means (Independent Samples)<\/p>\n
(x1 \u2013 x2) \u00b1 t\u03b12s12n1+ s22n2Note: t\u03b12 is found using the smaller of n1-1 or n2-1 degrees of freedom.<\/p>\n
Chapter 12: Additional Inferential Procedures<\/p>\n
Chi-Square Procedures<\/p>\n
Expected Counts (when testing for goodness of fit)<\/p>\n
\u0395i = \u03bci = npi for i = 1, 2, \u2026, k<\/p>\n
Expected frequencies (when testing for independence or homogeneity of proportions)<\/p>\n
Expected frequency = (row total)(column total)table totalChi-Square Test Statistic<\/p>\n
02 = (observed-expected)2expected = (Oi – Ei)2 Ei i = 1, 2, \u2026, k<\/p>\n
All Ei \u2265 1 and no more than 20% less than 5.<\/p>\n
Tables:<\/p>\n
Table II<\/p>\n
Critical Values (CV) for Correlation Coefficient<\/p>\n
n CV<\/p>\n
3 0.997<\/p>\n
4 0.950<\/p>\n
5 0.878<\/p>\n
6 0.811<\/p>\n
7 0.754<\/p>\n
8 0.707<\/p>\n
9 0.666<\/p>\n
10 0.632<\/p>\n
11 0.602<\/p>\n
12 0.576<\/p>\n
13 0.553<\/p>\n
14 0.532<\/p>\n
15 0.514<\/p>\n
16 0.497<\/p>\n
17 0.482<\/p>\n
18 0.468<\/p>\n
19 0.456<\/p>\n
20 0.444<\/p>\n
21 0.433<\/p>\n
22 0.423<\/p>\n
23 0.413<\/p>\n
24 0.404<\/p>\n
25 0.396<\/p>\n
26 0.388<\/p>\n
27 0.381<\/p>\n
28 0.374<\/p>\n
29 0.367<\/p>\n
30 0.361<\/p>\n
Table VI<\/p>\n
Critical Values for Normal Probability Plots<\/p>\n
Sample Size, n Critical Value<\/p>\n
5 0.880<\/p>\n
6 0.888<\/p>\n
7 0.898<\/p>\n
8 0.906<\/p>\n
9 0.912<\/p>\n
10 0.918<\/p>\n
11 0.923<\/p>\n
12 0.928<\/p>\n
13 0.932<\/p>\n
14 0.935<\/p>\n
15 0.939<\/p>\n
16 0.941<\/p>\n
17 0.944<\/p>\n
18 0.946<\/p>\n
19 0.949<\/p>\n
20 0.951<\/p>\n
21 0.952<\/p>\n
22 0.954<\/p>\n
23 0.956<\/p>\n
24 0.957<\/p>\n
25 0.959<\/p>\n
30 0.960<\/p>\n","protected":false},"excerpt":{"rendered":"
Tables and Formulas for Sullivan, Statistics: Informed Decisions Using Data Chapter 2: Organizing and Summarizing Data Relative frequency = frequencysum<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-40876","post","type-post","status-publish","format-standard","hentry"],"yoast_head":"\n