Tables Table A Table B Table C Table D Table E 675

Transcription

1 BMTables.indd Page /15/11 4:25:16 PM user-s163 Tables Table A Standard Normal Probabilities Table B Random Digits Table C t Distribution Critical Values Table D Chi-square Distribution Critical Values Table E Critical Values of the Correlation r 675

2 BMTables.indd Page /15/11 4:25:16 PM user-s TABLES Table entry for z is the area under the standard Normal curve to the left of z. Table entry z TABLE A Standard Normal cumulative proportions z

3 BMTables.indd Page /15/11 4:25:16 PM user-s163 TABLES 677 Table entry for z is the area under the standard Normal curve to the left of z. Table entry z TABLE A Standard Normal cumulative proportions (continued) z

4 BMTables.indd Page /15/11 4:25:16 PM user-s TABLES TABLE B Random digits LINE

5 BMTables.indd Page /15/11 4:25:16 PM user-s163 Table entry for C is the critical value t* required for confidence level C. To approximate one- and two-sided P-values, compare the value of the t statistic with the critical values of t* that match the P-values given at the bottom of the table. Area C t* t* Tail area 1 C 2 TABLE C t distribution critical values CONFIDENCE LEVEL C DEGREES OF FREEDOM 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% z* One-sided P Two-sided P

6 BMTables.indd Page /15/11 4:25:17 PM user-s TABLES Table entry for p is the critical value x* with probability p lying to its right. Probability p χ* TABLE D Chi-square distribution critical values df p

7 BMTables.indd Page /15/11 4:25:17 PM user-s163 TABLES 681 Table entry for p is the critical value r* of the correlation coefficient r with probability p lying to its right. Probability p r* TABLE E Critical values of the correlation r UPPER TAIL PROBABILITY p n

8 FrontEndpapers.indd Page 2 11/15/11 3:01:53 PM user-s163 STATISTICS IN SUMMARY Plot your data: Stemplot, histogram Analyzing Data for One Variable Interpret what you see: Shape, center, spread, outliers Numerical summary? x and s, five-number summary? Density curve? Normal distribution? STATISTICS IN SUMMARY Plot your data: Scatterplot Analyzing Data for Two Variables Interpret what you see: Direction, form, strength. Linear? Numerical summary? x, y, s x, s y, and r? Regression line? STATISTICS IN SUMMARY One sample Mean (quantitative data) Chap. 18 t = x µ s/ n Test a claim Significance test Two samples Proportion (categorical data) Compare means (quantitative data) Chap. 20 Chap. 19 z = ˆp p0 p0(1 p0) n ( x1 x2) (µ1 µ2) t = s 2 1 n1 + s2 2 n2 State problem Compare proportions (categorical data) Chap. 21 z = ˆp 1 ˆp 2 ˆp(1 ˆp)( 1 n1 + 1 n2 ) ˆp = pooled proportion Mean (quantitative data) Chap. 18 x ± t s n One sample Estimate a parameter Confidence interval Proportion (categorical data) Difference of means (quantitative data) Chap. 20 Chap. 19 ˆp ± z ˆp(1 ˆp) n ( x 1 x 2) ± t s 2 1 n 1 + s2 2 n 2 (use plus four) Two samples Difference of proportions (categorical data) Chap. 21 (ˆp 1 ˆp 2) ± z ˆp 1(1 ˆp 1) ˆp2(1 ˆp2) + n 1 n 2 (use plus four)

9 FrontEndpapers.indd Page 3 11/15/11 3:01:53 PM user-s163 ORGANIZING A STATISTICAL PROBLEM: A Four-Step Process STATE: What is the practical question, in the context of the real-world setting? PLAN: What specific statistical operations does this problem call for? SOLVE: Make the graphs and carry out the calculations needed for this problem. CONCLUDE: Give your practical conclusion in the setting of the real-world problem. CONFIDENCE INTERVALS: The Four-Step Process STATE: What is the practical question that requires estimating a parameter? PLAN: Identify the parameter, choose a level of confidence, and select the type of confidence interval that fits your situation. SOLVE: Carry out the work in two phases: 1. Check the conditions for the interval you plan to use. 2. Calculate the confidence interval. CONCLUDE: Return to the practical question to describe your results in this setting. TESTS OF SIGNIFICANCE: A Four-Step Process STATE: What is the practical question that requires a statistical test? PLAN: Identify the parameter, state null and alternative hypotheses, and choose the type of test that fits your situation. SOLVE: Carry out the test in three phases: 1. Check the conditions for the test you plan to use. 2. Calculate the test statistic. 3. Find the P-value. CONCLUDE: Return to the practical question to describe your results in this setting.