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## Quantitative Business Analysis Probability and Statistics

by: Mr. Jamey Collins

122

0

9

# Quantitative Business Analysis Probability and Statistics ISDS 361A

Marketplace > California State University - Fullerton > Info Systems & Decision Sciences > ISDS 361A > Quantitative Business Analysis Probability and Statistics
Mr. Jamey Collins
Cal State Fullerton
GPA 3.7

Panayiotis Skordi

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COURSE
PROF.
Panayiotis Skordi
TYPE
Class Notes
PAGES
9
WORDS
KARMA
25 ?

## Popular in Info Systems & Decision Sciences

This 9 page Class Notes was uploaded by Mr. Jamey Collins on Wednesday September 30, 2015. The Class Notes belongs to ISDS 361A at California State University - Fullerton taught by Panayiotis Skordi in Fall. Since its upload, it has received 122 views. For similar materials see /class/217079/isds-361a-california-state-university-fullerton in Info Systems & Decision Sciences at California State University - Fullerton.

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Date Created: 09/30/15
SAMPLEMEAN f Ciw n n POPULA T I ONMEAN N N N 1 22 DISCRETE PROBABILITY DIS TRIB U T I 0N MEAN u x xi x1Pltxa x2Pltx2 anltxn SAMPLE VARIANCE 2 S222 x 2xl f2x2 f2x3 f2xn f2 quot 1 n l n in2 xi2 1 x2x2x2 quotx2x1x2x3xn2 S2 n 1 2 3 V n quot 1 n l POPULATION VARIAN CE N xi 2 02 Z Z x1 2x2 2 xN 2 N AN i 2 xi Nx2 11 x2x2x2 x2 x1x2x3xN2 02 i1 1 N 1 2 3 N N A A FREQUENCY Grouped Data DISTRIBUTION VARIANCE m 2 I 2 x f 2 x1 my x2 4ij xm 4m n 1 n 1 M 2 x x x x n xlzflx fzx f3xm 222 322 mfm 2 S 2 2x311 S 11 7 n 1 n 1 DISCRETE RANDOM VARIABLE VARIANCE 02 n xi u2Pxlx1 u2Px1x2 ugt2Px2ltxn u2Pltxn 02 Zx3Px 2 1391 Empirical Rule Rule of Thumb 68 of the data values will be within 1 SD of the mean 95 of the data values will be within 2 SD of the mean 997 of the data values will lie within 3 SD of the mean Chebyshefs Theorem The proportion of observations that lie within k standard deviations of the mean is at least 1 1 F for kgt1 Coefficient of Variation Population coef cient of variation CV Sample coef cient of variation CV PERM U TA T IONS C 0MBINA T I ONS n r n Cr 2 n r n rr BINOMIAL DISTRIBUTION n r nir I9 9 PMquot n rr The mean L1 for a binomial probability distribution unp 2 and the varlance 039 1s 2 0 npq CON FIDENCE INTERVALS Q 10 40 2 TEST IS 039 SD POPULATION SD UCL x 2 E KNOWN SD LCL J za 7 4 xZ g a T TEST 2 TEST UCL I 1L UCLT i A J x 2 J LCin I HL LCin z i 2 J xZ MARGIN 0F ERROR SD E 2J E z E SD SD M SCENARIO HO u H1 u 4 TwoTail Hypothesis Test Reject H0 Reject H0 Do Not Reject H0 Z tdf tdf 2 A SCENARIOZ H0 u S H1 u gt OneT ail Hypothesis Test Reject H0 Do Not Reject Ho l Zd tjf SCENARIO3 HO y 2 H1 y lt OneT ail Hypothesis Test RejectHo Do Not Reject Ho ONE SAMPLE HYPOTHESIS TESTING 2 TEST IS a z CRITICAL FROM 2 POPULATION SD TABLES KNOWN 7 H TS in SD R 4 Va T TEST 2 TEST T CRITICAL FROM T 2 CRITICAL FROM 2 TABLES WITH n71 TABLES DEGREES OF FREEDOM fi Hn Y Min TS 7 SD TS 7 sy J 5 TWO SAMPLE HYPOTHESIS TESTING IS AT LEAST 0 2 TEST ARE 71 amp OquotZ POPULATION SD39s Z CRILIA ESROM Z KNOWN HM rmquot 9 439 5 2 TEST A z CRITICAL FROM 2 1 Z POPULATION SD39S TfBLES m TX2HM TIME S D 0 3M 86 6 a T TEST T TEST T CRITICAL FROM T TABLES T CRITICAL FROM T TABLES WITH WITH DEGREES OF FREEDOM n1 n2 7 2 2 DEGREES OF FREEDOM i quotI quot2 2 2 2 2 L L S n 71 n2 71 Summarizing the z scores for Various Levels of a P Value This is the smallest value of signi cance at which the null hypothesis is rejected Onetail test pValue For a onetail test with rejection region to the right the pValue will be the area to the right of the test statistic E g if the test statistic is 178 the pValue will be 375 Do NOT reject Ho 0 178 04625 39050462 5003 75 T wotail test p Value Using above example remember to multiply area by 2 the answer will be 75 Ifthe pValue oc we will reject the null hypothesis If the pValue gt0c we will not reject the null hypothesis Type 1 Error Level of signi cance alpha Correct null hypothesis but reject it Type 2 Error Null hypothesis is false but do not reject it Cannot accept Null Hypothesis Pg 196

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