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by: Nabila Reza

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# IE 330 review notes IE 330

Nabila Reza
Purdue
GPA 3.2

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Review notes
COURSE
Probability And Statistics In Engineering II
PROF.
Roshan Nateghi
TYPE
Study Guide
PAGES
12
WORDS
CONCEPTS
IE 330
KARMA
50 ?

## Popular in Industrial Engineering

This 12 page Study Guide was uploaded by Nabila Reza on Monday February 22, 2016. The Study Guide belongs to IE 330 at 1 MDSS-SGSLM-Langley AFB Advanced Education in General Dentistry 12 Months taught by Roshan Nateghi in Spring 2016. Since its upload, it has received 28 views. For similar materials see Probability And Statistics In Engineering II in Industrial Engineering at 1 MDSS-SGSLM-Langley AFB Advanced Education in General Dentistry 12 Months.

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Date Created: 02/22/16
Summary table for IE 330 Standard deviation for sample: Standard deviation for population :  2 V   n Z score when population standard deviation is given : T score when sample standard deviation is given: Confidence interval – Mean • Variance known – use the standard normal distribution • Variance unknown – use the t distribution     P   z  /2  1 x  z /2    n  n  s  s P  t  /2,n1   x t /2,1    n  n Standard error :   /2  E; wxhere E    n number of observations : 2 n   z /2  E   Confidence interval on variance and standard deviation : n1 s 2 1 2 n s    2    2 2  /2,n1  n 1 /2, 1 Confidence interval on population proportion : p(1-p ) V(p )  n  p(1- p)  p(1- p) P  z  /2 n ˆ    pzn/2     Prediction interval : 1 1 x t  /2,n1 1 X n1 x1t /2,n1  n n • Note that constructing confidence intervals requires our IID assumption plus the assumption of normality. Chapter 9 Reject H0 Accept H0 There is a 100(α)% chance we should havP(Type 2 error) = β reject H0. There is a 100(β)% chance we actually should have P(Type 2 error) = 0 rejected H0. Hypothesis test on population mean, two-sided, variance known H :    0 0 H :   1 0 X  0 Z0 reject H0if Z 0 z  /2or if Z z1 /2  / n P ype 1 error  p-value can be obtained from computer or Table II. P ype 2 error  (by computer or Chart VIa or b) Power 1   Hypothesis test on population mean, one-sided, variance known H 0   0 H 1  0 Z  X  0 rejectz if Z 0  / n 0 0 1 P ype 1 error  p-value can be obtained from computer or Table II. P Type 2 error   (by computer or Chart VIc or d)   Power 1   Hypothesis test on population mean, one-sided, variance known H :    0 0 H 1  0 Z  X  0 rejectz if Z 0  / n 0 0  P ype 1 error  p-value can be obtained from computer or Table II. P ype 2 error  (by computer or Chart VIc or d) Power 1   Hypothesis test on population mean, two-sided, variance unknown H :    0 0 H 1   0 X  0 T  reject H0if T  t  /2,n1 i Tn t/2, 1 s/ n P ype 1 error  p-value can be obtained from computer or Table IV. P ype 2 error  (by computer or Chart VIe or f) Power 1   Hypothesis test on population mean, one-sided, variance unknown H 0   0 H :    1 0 X  0 T  rejectH 0f T ,n1 s/ n P Type 1 error    p-value can be obtained from computer or Table IV. P ype 2 error  (by computer or Chart VIg or h) Power 1   Hypothesis test on population mean, one-sided, variance unknown H :0  0 H 1  0 X  0 T  reject Ht 0f T   ,n1 s/ n P ype 1 error  p-value can be obtained from computer or Table IV. P ype 2 error   (by computer or Chart VIg or h) Power 1   Hypothesis test on population variance, two-sided H :  2  2 0 0 H :   2 1 0 n1S  2  0 2 reject H0if  0  1 /2,n1if 0 n 2/2, 1  0 P ype 1 error  p-value can be obtained from computer or Table III. P Type 2 error   (by computer or Chart VIi or j)   Power 1  Hypothesis test on standard deviation, two-sided H :   0 0 H 1   0 2 n1S 2 2 2 2 2  0 2 reject H0if  0  1 /2,n1 if 0 n /2, 1 0 P ype 1 error  p-value can be obtained from computer or Table III. P ype 2 error  (by computer or Chart VIi or j) Power 1  Hypothesis test on population variance, one-sided H :0 2 02 H :  2  2 1 0 n1 S 2  2 reject H if    2 0  2 0 0 ,n1 0 P ype 1 error  p-value can be obtained from computer or Table III. P Type 2 error   (by computer or Chart VIk or l)   Power 1   2 2 H 0   0 2 2 H 1   0 2 2 n1  2 2  0 2 reject H 0f   0 1n 1  0 P ype 1 error  p-value can be obtained from computer or Table III. P ype 2 error   (by computer or Chart VIk or l) Power 1   H 0 p p0 H 1 p p0 X np Z 0 0 reject H0if Z 0 z  /2or if Z0 z1 /2 np 1 p  0 0 P ype 1 error  p-value can be obtained from computer or Table II. P ype 2 error  (by computer or Chart VIa or b) Power 1  H 0 p p0 H 1 p p0 X np Z 0 0 rejezt H0if Z 0 1 np01 p0  P ype 1 error  p-value can be obtained from computer or Table II. P ype 2 error   (by computer or Chart VIc or d) Power 1   H 0 p p0 H : p p 1 0 X np 0 Z 0 rejezt H0if Z 0  np01 p0  P ype 1 error  p-value can be obtained from computer or Table II. P ype 2 error   (by computer or Chart VIc or d) Power 1   Chi square test Hypothesis tests on differences in means, variance known X X1  2  0 Z  0 2 2   1 2  n n 1 2 Hypothesis tests on difference in means, same unknown variance X X1  2  0 T  0 1 1 S  p n n 1 2 Confidence intervals on differences in means, variance known  2 2 2 2 P   X z 1 2      X  X z   2  1   1 2 /2 n1 n2 1 2 1 2 1  /21 n2   Confidence intervals on differences in means, equal unknown variance  1 1 1 1 P  1 X2t/212 p n2n  1 2  1 2X /212 p n2n     1 2 1 2 Confidence intervals on differences in means, unequal unknown variance  2 2  2 2 P  1 X 2t /2,1 s2 1 2 X1 2 /2,s1 s2     1 n2 n1 n2 • for our “normal” hypothesis test, our test statistic for unequal variance unknown is: * X 1 X 2  0 T 0 2 2 S 1 2  n 1 2 • For the paired t-test, our test statistic is: D * 0 T 0 S n / D Confidence intervals on the difference between two population proportions p  p ˆ  1p  p  p  p  z 1 1  2 2  p  p 1 2 /2 n n 1 2 1 2 p1 p ˆ1  1p2  pˆ2 p1 p 2 p  1  z2 1/2  n1 n2 created by Nabila Reza

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