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Course: STATISTICS stat 410, Spring 2011
School: University of Illinois,...
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University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #1(due Friday, September 4, by 4:00 p.m.)1.Let &gt; 0 and let X be a random variable with the probability density functionf(x) =x +1,x &gt; 1,zero otherwise.Let W = ln ( X ). What is the probability distribution of W ?2.Le
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #1(due Friday, September 4, by 4:00 p.m.)1.Let &gt; 0 and let X be a random variable with the probability density functionf(x) =x +1x &gt; 1,,zero otherwise.Let W = ln ( X ). What is the probability distribution of W ?x&gt;1d
University of Illinois, Urbana Champaign - STATISTICS - stat 410
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #2(due Friday, September 11, by 4:00 p.m.)1.Let X 1 , X 2 , , X n be a random sample of sizeprobability density functionf X (x) = f X ( x ; ) = ( 1 ) 2 a)ln xx,nfrom the distribution withx &gt; 1, &gt; 1.We already know
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #2(due Friday, September 11, by 4:00 p.m.)1.Let X 1 , X 2 , , X n be a random sample of sizeprobability density functionf X (x) = f X ( x ; ) = ( 1 ) 2 a)ln xxn,from the distribution withx &gt; 1, &gt; 1.We already know
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #3(due Friday, September 18, by 4:00 p.m.)1.Let X 1 , X 2 , , X n be a random sample of sizeprobability density functionf X (x) = f X ( x ; ) = ( 1 ) 2 ln xxnfrom the distribution with &gt; 1.x &gt; 1,,a)Find the suffic
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #3(due Friday, September 18, by 4:00 p.m.)1.Let X 1 , X 2 , , X n be a random sample of sizeprobability density functionf X (x) = f X ( x ; ) = ( 1 ) 2 a)ln xxnfrom the distribution withx &gt; 1,, &gt; 1.Find the suffic
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2005Homework #4(due Friday, September 25, by 4:00 p.m.)From the textbook:6.4-86.4-106.8-26.5-26.4-126.8-46.4-186.8-66.5-4Hint: Equal variances10.The National Security Agency (NSA) hires you to compute a 95% confidenceinterval
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2005Homework #4(due Friday, September 25, by 4:00 p.m.)From the textbook:6.4-8a) x = 46.42;b) s 2 = 41.682, s 6.456, t 0.05 ( 4 ) = 2.132,46.42 2.132 6.4565or46.42 6.156or( 40.264, 52.576 ).6.4-10t 0.10 ( 27 ) = 1.314,( 21.45
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #5(due Thursday, October 1, by 4:00 p.m.)From the textbook:6.6-26.6-46.6-86.6-106.7-26.7-46.7-126.7-186.8-12 if we believe the seed distributors claim;b)10.a) if we ignore the seed distributors claim.Let X have
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Homework #5(due Thursday, October 1, by 4:00 p.m.)From the textbook:6.6-2For these 9 weights, x = 20.90, s = 1.858.a)A point estimate for is s = 1.858.b)8 1.858 2,17.548 1.858 2 = [ 1.255, 3.559 ].2.180 c)8 1.858 2,15.518 1.858
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #6(due Friday, October 9, by 4:00 p.m.)1.Let a &gt; 0, &gt; 0 and let X 1 , X 2 , , X n be a random sample of sizedistribution with probability density functionf X (x) = f X ( x ; ) =aa x a 1 ,nfrom anfrom a0 &lt; x &lt; .Sup
University of Illinois, Urbana Champaign - STATISTICS - stat 410
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #7 (Answers)8.1-6H 0 : p = 1/6 vs. H 1 : p &lt; 1/6orH 0 : p 1/6 vs. H 1 : p &lt; 1/6Left tailed.n = 8000.a)The test statistic isz= = 0.05.b)y py1n0=80006.p 0 (1 p 0 )1 1 166n8000(The critical (rejection) reg
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Homework #8Fall 2009(due Friday, October 23, by 4:00 p.m.)1.In a random sample of 100 Hawk &amp; Hummingbird Airline (HHA) direct flightsfrom New York to Boston, the average number of passengers was 56.3, withsample standard deviation 11.33.a)
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #8(due Friday, October 23, by 4:00 p.m.)1.In a random sample of 100 Hawk &amp; Hummingbird Airline (HHA) direct flightsfrom New York to Boston, the average number of passengers was 56.3, withsample standard deviation 11.33.X
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #9(due Friday, October 30, by 4:00 p.m.)From the textbook:8.2-169.1-49.1-69.1-109.1-79.1-127.Let X 1 , X 2 , , X 25 be a random sample from a N ( , 100 ) population,and suppose the null hypothesis H 0 : = 100 is to b
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #9(due Friday, October 30, by 4:00 p.m.)From the textbook:8.2-16H 0 : 2 = 30 vs. H 1 : 2 = 80.Right tailed.Recall: If X 1 , X 2 , , X n are i.i.d. N ( , 2 ), thena)Test Statistic:2 =2is 2 ( n 1 ).(n 1) s 2 = 18 s 2
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Homework #10Fall 2009(due Thursday, November 5, by 4:00 p.m.)1 2.Bert and Ernie noticed that thefollowing are satisfied whenCookie Monster eats cookies:(a)the number of cookies eaten duringnon-overlapping time intervals areindependent;
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Homework #10Fall 2009(due Thursday, November 5, by 4:00 p.m.)1 2.Bert and Ernie noticed that thefollowing are satisfied whenCookie Monster eats cookies:(a)the number of cookies eaten duringnon-overlapping time intervals areindependent;
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Homework #11Fall 2009(due Wednesday, November 13, by 4:00 p.m.)1.Let &gt; 0 and let X 1 , X 2 , , X n be independent random variables, each withthe probability density function +1f(x) = x0x 1.x &lt;1We wish to test H 0 : = 1 vs. H 1 : &gt; 1.
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #11(due Friday, November 13, by 4:00 p.m.)1.Let &gt; 0 and let X 1 , X 2 , , X n be independent random variables, each withthe probability density function +1f(x) = x0x 1.x &lt;1We wish to test H 0 : = 1 vs. H 1 : &gt; 1.a)
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #12(due Friday, November 20, by 4:00 p.m.)8.6-195(O E )3237.268.423.446.2360.038710.09883264318322859.2E45532210.432883E7188.8O3624.845.615.630.8300240.246154 0.031169 0.4444442000.649324 0
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #13(due Friday, December 4, by 4:00 p.m.)1.Seventy percent of the light aircraft that disappear while in flight in Neverlandare subsequently discovered. Of the aircraft that are discovered, 60% have anemergency locator, wh
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Homework #13(due Friday, December 4, by 4:00 p.m.)1.Seventy percent of the light aircraft that disappear while in flight in Neverlandare subsequently discovered. Of the aircraft that are discovered, 60% have anemergency locator, wh
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Homework #14Fall 2009(due Wednesday, December 9, by 4:30 p.m.)1.When correctly adjusted, a machine that makes widgets operates with a 5% defectiverate. However, there is a 10% chance that a disgruntled employee kicks the machine,in which ca
University of Illinois, Urbana Champaign - STATISTICS - stat 410
University of Illinois, Urbana Champaign - STATISTICS - stat 410
1.Let X 1 , X 2 , , X n be a random sample from the distribution with probabilitydensity functionf (x ) = 4 x 3 e x4 &gt; 0.x&gt;0a)Find the sufficient statistic Y = u ( X 1 , X 2 , , X n ) for .b)Obtain the maximum likelihood estimator of ,c)Isa c
University of Illinois, Urbana Champaign - STATISTICS - stat 410
Practice Problems1.The label on 1-gallon can of paint states that the amount of paint in the can issufficient to paint at least 400 square feet (on average). Suppose the amount ofcoverage is approximately normally distributed, and the overall standard
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Name _Quiz 1(3 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.Metaltech Industries manufactures carbide drill tips used in drilling oil wells.The lif
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009NameANSWERS.Quiz 1(3 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.Metaltech Industries manufactures carbide drill tips used in drilling oil wells.
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Name _Quiz 2(3 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.At Anytown State University, the population standard deviation of the SAT scoresof ente
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009NameANSWERS.Quiz 2(3 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.At Anytown State University, the population standard deviation of the SAT scores
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Name _Version AQuiz 3(3 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.a) (1) Suppose we Do NOT Reject H 0 for = 0.05. Then for = 0.10, we _.( Circle o
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009NameANSWERS.Version AQuiz 3(3 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.a) (1) Suppose we Do NOT Reject H 0 for = 0.05. Then for = 0.10, we _.(
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Name _Version BQuiz 3(3 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.a) (1) Suppose we Do NOT Reject H 0 for = 0.05. Then for = 0.01, we _.( Circle o
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009NameANSWERS.Version BQuiz 3(3 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.a) (1) Suppose we Do NOT Reject H 0 for = 0.05. Then for = 0.01, we _.(
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Name _Version AQuiz 4(5 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.At Anytown College, the administration would like the students grade distribut
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009NameANSWERS.Version AQuiz 4(5 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.At Anytown College, the administration would like the students grade d
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Name _Version BQuiz 4(5 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.At Anytown College, the administration would like the students grade distribut
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009NameANSWERS.Version BQuiz 4(5 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.At Anytown College, the administration would like the students grade d
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Name _Version AQuiz 5(5 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.A travel agent randomly sampled individuals in her target market to determine
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009NameANSWERS.Version AQuiz 5(5 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.A travel agent randomly sampled individuals in her target market to de
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009Name _Version BQuiz 5(5 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.A travel agent randomly sampled individuals in her target market to determine
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409Fall 2009NameANSWERS.Version BQuiz 5(5 points)Be sure to show all your work, your partial credit might depend on it.No credit will be given without supporting work.1.A travel agent randomly sampled individuals in her target market to de
University of Illinois, Urbana Champaign - STATISTICS - stat 410
Cumulative Binomial Probabilities p n2Cumulative Binomial Probabilities p0.60 0.160 0.640 0.064 0.352 0.784 0.026 0.179 0.525 0.870 0.010 0.087 0.317 0.663 0.922 0.004 0.041 0.179 0.456 0.767 0.953 0.002 0.019 0.096 0.290 0.580 0.841 0.972 0.001 0.009
University of Illinois, Urbana Champaign - STATISTICS - stat 410
Left tailed testH 0 : p = p0vs.H 1 : p &lt; p0If H 0 is TRUE :Use p 0 .Reject H 0Do NOT Reject H 0Type I ErrorCorrect decisiona0a+1nRejection Rule for a Left tailed test:Find a such that P( Y a ) = CDF @ a .( using Binomial ( n , p 0 ) tables
University of Illinois, Urbana Champaign - STATISTICS - stat 410
Chapter 6Estimation6.1Sample Characteristics6.12 (a) x =(b) s2 =4= 1.333;388= 1.275.696.14 (a) x = 1.711, s = 0.486;(b) and (d) graphs.0.80.70.60.50.40.30.20.10.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7123456Figure 6.14: (b) Female un
University of Illinois, Urbana Champaign - STATISTICS - stat 410
Chapter 8Tests of Statistical Hypotheses8.1Tests about Proportions8.12 (a) C = cfw_x : x = 0, 1, 2;(b) = P (X = 0, 1, 2; p = 0.6)= (0.4)4 + 4(0.6)(0.4)3 + 6(0.6)2 (0.4)2 = 0.5248;= P (X = 3, 4; p = 0.4)= 4(0.4)3 (0.6) + (0.4)4 = 0.1792.OR(a ) C
University of Illinois, Urbana Champaign - STATISTICS - stat 410
Consider a coin being tossed 20 times.There are 2 20 = 1,048,576 possible outcomes (samples).Suppose we wish to test whether the coin is fair or not.We can rank all these outcomes (samples) from 20 C 10 = 184,756 best outcomes(samples) with 10 Hs and
University of Illinois, Urbana Champaign - STATISTICS - stat 410
STAT 409 / MATH 409Monday, Wednesday, FridayInstructor:Office:E-mail:Office hours:Text:Fall 20092:00 2:50 p.m.103 Talbot LaboratoryAlexey Stepanov101-A Illini Hallstepanov@illinois.eduph.:265-6550Monday 3:30 4:30 p.m., Thursday 1:30 3:00 p.
University of Illinois, Urbana Champaign - STATISTICS - stat 410
William Gosset(1876-1937)Thet DistributionEXCEL: = TINV ( , v ) = TDIST ( t , v , 1 ) = TDIST ( t , v , 2 ) gives gives givest2for t distribution with v degrees of freedom the upper tail probability for t distribution with v degrees of freedom, P (
Bilkent University - DSB - 243
BLECK NVERSTES REKTRLNDENniversitemiz Sosyal Bilimler Enstitsne 2011-2012 Eitim retim Yl Gz Yarylnda TezliYksek Lisans Programlarna renci alnacaktr.BAVURU ARTLARI1.2.ALES snavndan; bavurulan programn n grd puan trnde yksek lisans iin en az 55 puana
University of South Africa - MNG 2016 - 2016
# 2008 University of South AfricaAll rights reservedPrinted and published by theUniversity of South AfricaMuckleneuk, PretoriaMNG2016/1/2009201198309153MNB-StylCONTENTSPagePREFACEivTOPIC 1: THE NATURE OF GENERAL MANAGEMENT1STUDY UNIT 1:INTR
University of South Africa - MNG 2016 - 2016
9/19/2011MNG 2016General ManagementPresenting Lecturer:MRS K STANDERstandk@unisa.ac.zaOBJECTIVES OF THE GROUP DISCUSSION CLASS1. AN OVERVIEW OF THE CONTENT OF THIS MODULE.2. PREPARATION FOR THE EXAMINATION.3. THE FORMAT OF THE EXAMINATION PAPER.
University of South Africa - MNG 2016 - 2016
University of South Africa - MNG 2016 - 2016
University of South Africa - MNG 2016 - 2016
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University of South Africa - MNG 2016 - 2016
University of South Africa - MNG 2016 - 2016
University of South Africa - MNG 2016 - 2016