NEGATIVE z Scores. TABLE A-2 Standard Normal (z) Distribution: Cumulative Area from the LEFT. (continued)

Transcription

1 NEGATIVE z Score z 0 TALE A- Standard Normal (z) Ditribution: Cumulative Area from the LEFT z and lower * * NOTE: For value of z below -3.49, ue for the area. *Ue thee common value that reult from interpolation: (continued) z Score Area

2 POSITIVE z Score 0 z TALE A- (continued) Cumulative Area from the LEFT z * * and up.9999 NOTE: For value of z above 3.49, ue for the area. *Ue thee common value that reult from interpolation: z core Area Common Critical Value Confidence Level Critical Value

3 TALE A-3 t Ditribution: Critical t Value Degree of Freedom Area in One Tail Area in Two Tail Large

4 TALE A-4 Chi-Square (x ) Ditribution Formula and Table by Mario F. Triola Copyright 018 Pearon Education, Inc. Area to the Right of the Critical Value Degree of Freedom Source: From Donald. Owen, Handbook of Statitical Table. Degree of Freedom n - 1 Confidence Interval or Hypothei Tet for a tandard deviation or variance k - 1 Goodne-of-fit tet with k different categorie (r - 1)(c - 1) Contingency table tet with r row and c column k - 1 Krukal-Walli tet with k different ample

5 Formula and Table by Mario F. Triola Copyright 018 Pearon Education, Inc. Ch. 3: Decriptive Statitic x = Σx n x = Σ1f # x Σf Mean = Σ1x - x n - 1 = n 1Σx - 1Σx n - 1 Mean (frequency table) Standard deviation = n 3 Σ1f # x 4-3 Σ1f # x 4 n - 1 variance = Ch. 4: Probability Standard deviation (hortcut) Standard deviation (frequency table) P1A or = P1A + P1 if A, are mutually excluive P1A or = P1A + P1 - P1A and if A, are not mutually excluive P1A and = P1A # P1 if A, are independent P1A and = P1A # P1 0 A if A, are dependent P1A = 1 - P1A Rule of complement n! np r = Permutation (no element alike) - r! n! Permutation (n n 1! n! c n k! 1 alike, c) n! nc r = Combination - r! r! Ch. 5: Probability Ditribution m = Σ 3x # P1x 4 Mean (prob. dit.) = Σ 3x # P1x 4 - m Standard deviation (prob. dit.) n! P1x = inomial probability m = n # p = n # p # q = # p # q # P1x = mx e -m x! - x! x! # p x # q n-x Mean (binomial) Variance (binomial) Standard deviation (binomial) Poion ditribution where e =.7188 Ch. 7: Confidence Interval (one population) pn - E 6 p 6 pn + E Proportion pnqn where E = z a> n x - E 6 m 6 x + E Mean where E = t a> ( unknown) or E = z a> ( known) x R - 1 x L Ch. 7: Sample Size Determination n = 3z a>4 0.5 E Proportion Variance n = 3z a>4 pnqn E Proportion (pn and qn are known) n = J z a> E R Mean Ch. 8: Tet Statitic (one population) z = pn - p pq n t = x - m z = x - m x = - 1 Proportion one population Mean one population ( unknown) Mean one population ( known) Standard deviation or variance one population Ch. 6: Normal Ditribution z = x - m or x - x Standard core m x = m Central limit theorem x = Central limit theorem (Standard error) n

6 Formula and Table by Mario F. Triola Copyright 018 Pearon Education, Inc. Ch. 9: Confidence Interval (two population) 1 pn 1 - pn - E 6 1 p 1 - p 6 1 pn 1 - pn + E where E = z a> pn 1 qn 1 n 1 + pn qn n 1x 1 - x - E 6 1m 1 - m 6 1x 1 - x + E (Indep.) (df = maller of 1 where E = t a> + n 1-1, n - 1) n 1 n ( 1 and unknown and not aumed equal) p E = t a> + p 1df = n 1 + n - n 1 n p = ( 1 and unknown but aumed equal) 1 E = z a> + n 1 n ( 1, known) d - E 6 m d 6 d + E (Matched pair) where E = t a> d 1df = n - 1 Ch. 9: Tet Statitic (two population) z = 1pn 1 - pn - 1p 1 - p p q + p q n 1 n t = 1x 1 - x - 1m 1 - m 1 n 1 + n Two proportion p = x 1 + x n 1 + n df = maller of n 1-1, n - 1 Two mean independent; 1 and unknown, and not aumed equal. t = 1x 1 - x - 1m 1 - m p + p n 1 n 1df = n 1 + n - p = n 1 + n - Two mean independent; 1 and unknown, but aumed equal. z = 1x 1 - x - 1m 1 - m t = d - m d d F = 1 1 n 1 + n Two mean independent; 1, known. Two mean matched pair (df = n - 1) Standard deviation or variance two population (where 1 Ú ) Ch. 10: Linear Correlation/Regreion Correlation r = Slope: nσxy - 1Σx1Σy n1σx - 1Σx n1σy - 1Σy or r = g 1z x z y n - 1 b 1 = y-intercept: where z x = z core for x z y = z core for y nσxy - 1Σx1Σy n 1Σx - 1Σx or b 1 = r y x b 0 = y - b 1 x or b 0 = 1Σy1Σx - 1Σx1Σxy n 1Σx - 1Σx yn = b 0 + b 1 x Etimated eq. of regreion line explained variation r = total variation e = Σ1y - yn n - or Σy - b 0 Σy - b 1 Σxy n - yn - E 6 y 6 yn + E Prediction interval where E = t a> e n + n1x 0 - x n1σx - 1Σx Ch. 11: Goodne-of-Fit and Contingency Table 1O - E x = g E Goodne-of-fit (df = k - 1) 1O - E x = g E Contingency table [df = (r - 1)(c - 1)] 1row total1column total where E = 1grand total x = 1 0 b - c 0-1 b + c Ch. 1: One-Way Analyi of Variance McNemar tet for matched pair 1df = 1 Procedure for teting H 0 : m 1 = m = m 3 = c 1. Ue oftware or calculator to obtain reult.. Identify the P-value. 3. Form concluion: If P-value a, reject the null hypothei of equal mean. If P-value 7 a, fail to reject the null hypothei of equal mean. Ch. 1: Two-Way Analyi of Variance Procedure: 1. Ue oftware or a calculator to obtain reult.. Tet H 0 : There i no interaction between the row factor and column factor. 3. Stop if H 0 from Step i rejected. If H 0 from Step i not rejected (o there doe not appear to be an interaction effect), proceed with thee two tet: Tet for effect from the row factor. Tet for effect from the column factor.

7 Formula and Table by Mario F. Triola Copyright 018 Pearon Education, Inc. Ch. 13: Nonparametric Tet 1x > z = z = T - n + 1 >4 n + 11n Sign tet for n 7 5 z = R - m R - n n + 1 R = R n 1 n 1 + n H = Wilcoxon igned rank (matched pair and n 7 30) Wilcoxon rank-um (two independent ample) 1 N1N + 1 ar 1 + R + g + R k b - 31N + 1 n 1 n n k Krukal-Walli (chi-quare df = k - 1) 6Σd r = 1 - n - 1 acritical value for n 7 30: z = G - m G G = Ch. 14: Control Chart R chart: Plot ample range UCL: D 4 R Centerline: R LCL: D 3 R x chart: Plot ample mean UCL: x + A R Centerline: x LCL: x - A R Rank correlation p chart: Plot ample proportion p q UCL: p + 3 n Centerline: p p q LCL: p - 3 n { z - 1 b G - a n + 1b n 1 + n 1n 1 n 1n 1 n - n 1 - n 1 + n 1 + n - 1 Run tet for n 7 0 TALE A-6 Critical Value of the Pearon Correlation Coefficient r n a =.05 a = NOTE: To tet H 0 : r = 0 (no correlation) againt H 1 : r 0 (correlation), reject H 0 if the abolute value of r i greater than or equal to the critical value in the table. Control Chart Contant Subgroup Size n D 3 D 4 A Inference about M: chooing between t and normal ditribution t ditribution: not known and normally ditributed population or not known and n 7 30 Normal ditribution: known and normally ditributed population or known and n 7 30 Nonparametric method or boottrapping: Population not normally ditributed and n 30

8 Procedure for Hypothei Tet 1. Identify the Claim Identify the claim to be teted and expre it in ymbolic form.. Give Symbolic Form Give the ymbolic form that mut be true when the original claim i fale. 3. Identify Null and Alternative Hypothei Conider the two ymbolic expreion obtained o far: Alternative hypothei H 1 i the one NOT containing equality, o H 1 ue the ymbol. or, or Þ. Null hypothei H 0 i the ymbolic expreion that the parameter equal the fixed value being conidered. 4. Select Significance Level Select the ignificance level A baed on the erioune of a type I error. Make A mall if the conequence of rejecting a true H 0 are evere. The value of 0.05 and 0.01 are very common. 5. Identify the Tet Statitic Identify the tet tatitic that i relevant to the tet and determine it ampling ditribution (uch a normal, t, chi-quare). P-Value Method 6. Find Value Find the value of the tet tatitic and the P-value (ee Figure 8-3). Draw a graph and how the tet tatitic and P-value. Critical Value Method 6. Find Value Find the value of the tet tatitic and the critical value. Draw a graph howing the tet tatitic, critical value() and critical region. 7. Make a Deciion Reject H 0 if P-value # a. Fail to reject H 0 if P-value. a. 7. Make a Deciion Reject H 0 if the tet tatitic i in the critical region. Fail to reject H 0 if the tet tatitic i not in the critical region. 8. Retate Deciion in Nontechnical Term Retate thi previou deciion in imple nontechnical term, and addre the original claim. Finding P-Value Start Left-tailed What type of tet? Right-tailed Left I the tet tatitic to the right or left of center? Right P-value 5 area to the left of the tet tatitic P-value 5 twice the area to the left of the tet tatitic P-value 5 twice the area to the right of the tet tatitic P-value 5 area to the right of the tet tatitic