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This 4 page Class Notes was uploaded by Aileen Davis on Tuesday October 20, 2015. The Class Notes belongs to MATH0013 at Sierra College taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/225381/math0013-sierra-college in Mathematics (M) at Sierra College.
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Date Created: 10/20/15
and Notations Statistics ID Abe Mirza Formulas Symbols 2 u 2 039 s 12 Chi squared 2 2 Z amp or 7amp s EU x s an 72 N n n l nn 1 Range To Estimate 5 S T Variance 62 S2 Variance is the square of standard deviation Grouped Data Freq Table 2mm S quotzoxmwznmr quot7171 7 2f Empirical Rules If the boxplot is centered then we can apply the three following empirical rules 997 0o of data are within 3 S of the mean f 997 C i 3 S 3 95 f i 2 S 3 95 0o of data are within 2 S ofthe mean 7 68 C i S 3 68 0o of data are within 1 S ofthe mean f Z Score Z xix or Z2 s 039 0 2 2 Zgt2 Unusual Values Z lt 72 Ordinary Values 72 g Z g 2 Unusual Values Correrlation J5quot 39 2r quotnyzxzy Z 1Srgl anxtmx anytltzygt RegressionEquation yaxb aSlope byintercept Slopeam yitcbW n2x22x n2x22x Using the regression equation to estimate or predict y and x that are shown by y39 and x39 Multiplication Rule PA and B and C and PAPBPC Formulas Last Update 04042007 Addition Rule PA or B PA PB7pA and B Multiplication Rule PA and B and C and PAPBPC Discrete Probability Distribution x fcays PX xpoc Expected Value Mean u 2x px 2961706 Counting Factorial Number of ways n objects or subjects can be arranged I ll Combination Number of ways that x objects or subjects can be selected from n objects or subjects n The order in selection is not relevant an x n x Permutation Number of ways that x objects or subjects can be selected from n objects or subjects n n x The order in selection is relevant an Binomial Probability n Px an pquot1 pquot Mean u np St Dev a ln p1 p Pass x n fail p Desired probability n Total number of trials x Number of desired outcomes an Combination Rule p 1 p Px an pquot1 p quot7quot Non Standard Normal Probability NSNPD Conveiting a non standard value to standard value by using x x E Z u or Z o s Cut off point formula x fs z or x u039 z Fro nding Z you need to look it up on page 3 of the table Formulas Last Update 04042007 2 Estimating One Population A7 Point estimate Sample Mean 13 1 Point estimate Sample Proportion n E Margin of error E Margin of error Mean Proportion For Z use Table page 3 For t use Table page 4 Estimating Two Population A7 Point estimate Sample Mean E Margin of error Mean ul yz Prop01tion 131 132 1 y2cl cziE P1Pz1A71IA72iE 1H 1H 1311 i21gt132lt1 192gt n2 quot1 n2 Sample Size Determining for the Estimation of Population Mean p Proportion P 2 2 A A nZSE nZE p1 p If s is unknown the eStimate it by If i7 is unknown then estimate it by S Range 4 A p 05 Central Limit theorem 3 Z M 039 Formulas Last Update 04042007 3 Test of Hypothesis 4 Compute Test Statistics based on sample information from the following formulas z m To test the Mean 1 for large sample sizes s b IM To test the Mean 1 for n S 30 and when 039 is unknown s 17 Z To test populatlon proportlon P p1 p n d Z f1f21u11u2 2 2 s1 s2 quot1 quot2 Two independent population ul H2 JE57 d I For Paired Samples Sd 2 f 12 Observed Expected for Multinomial or Independency Test Formulas Last Update 04042007