Introduction to the Practice of Statistics Sixth Edition Moore, McCabe Section 5.1 Homework Answers


 Lorin Bridges
 1 years ago
 Views:
Transcription
1 Introduction to the Practice of Statistics Sixth Edition Moore, McCabe Section 5.1 Homework Answers 5.18 Attitudes toward drinking and behavior studies. Some of the methods in this section are approximations rather than exact probability results. We have given rules of thumb for safe use of these approximations. (a) You are interested in attitudes toward drinking among the 75 members of a fraternity. You choose 30 members at random to interview. One question is "Have you had five or more drinks at one time during the last week?" Suppose that in fact 30% of the 75 members would say "Yes." Explain why you cannot safely use the B(30, 0.3) distribution for the count X in your sample who say "Yes." The binomial distribution assumes that we have independence. In this case we do not, and the probabilities change too much for us to disregard the fact that we do not. P(drink) = 0.3, P(drink drink and drink and not drink and not drink and not drink and not drink) = and this is after only sampling five, by 20, the probability of success will not be close to 0.3. (b) The National AIDS Behavioral Surveys found that 0.2% (that's as a decimal fraction) of adult heterosexuals had both received a blood transfusion and had a sexual partner from a group at high risk of AIDS. Suppose that this national proportion holds for your region. Explain why you cannot safely use the Normal approximation for the sample proportion who fall in this group when you interview an SRS of 1000 adults. The criteria is np 10 and n(1 p) 10. The probability of success is (1000) = 2 is not greater than 10.
2 5.22 The ideal number of children. "What do you think is the ideal number of children for a family to have?" A Gallup Poll asked this question of 1016 randomly chosen adults. Almost half (49%) thought two children was ideal. 3 Suppose that p = 0.49 is exactly true for the population of all adults. Gallup announced a margin of error of ±3 percentage points for this poll. What is the probability that the sample proportion ˆp for an SRS of size n = 1016 falls between 0.46 and 0.52? You see that it is likely, but not certain, that polls like this give results that are correct within their margin of error. We will say more about margins of error in Chapter 6. A similar question was asked in chapter 4, section 3, n = 1016, p = 0.49, 1016(0.49) = (expected number of successes and 1016(0.51) = expected number of failures thus the distribution of this binomial situation resembles that of a normal distribution. Let X count the number of people that think 2 children is ideal. Sample space: {X 0, 1, 2,, 1016} Or Sample space { ˆp 0, 1/1016, 2/1016,, 1015/1016, 1} The sample spaces consist of 1017 values. 0.46(1016) = , 0.52(1016) = Here is what we want expressed as either a count or proportion: P(0.46 ˆp 0.52) P(467 X 528) You can see that all we can do is get an approximation to the question since you can not have a count of for example. P(467 X 528) = P(X 528) P(X 466) = = =binomdist(528, 1016, 0.49,true) binomdist(466,1016,0.49, true) Why did I change from 467 to 466? Because I want to include 467 in the calculation, and since I have a discrete distribution, I need to take away 466, 465, and so on. Normal Approximation  typically, in this scenario posed, most researchers will do a normal approximation and not the procedure for a binomial calculation.
3 Again we meet the criteria np 10 and n(1 p) 1016(0.49) = and 1016(0.51) = (1016) = , 0.52(1016) = P(0.46 ˆp 0.52) P(X ) P(X ) (0.49) P Z (0.49) P Z 1016 P(Z < 1.91)  P(Z < 1.91) Notice that this value is smaller than the one using the binomial routine. P(0.46 ˆp 0.52) PZ (0.49) PZ (0.49) 1016 P(Z < 1.91)  P(Z < 1.91) Notice that this value is smaller than the one using the binomial routine. Using a normal approximation  The sample size here is large and p is in the middle of the possible range of p values; [0, 1]. Thus the normal approximation above will be very close to actual. Below are the steps with continuity correction. P(X 528.5) P(X 466.5) (0.49) P Z P Z (0.49) 1016 P(Z < 1.924)  P(Z < )
4 5.24 How do the results depend on the sample size? Return to the Galiup Poll setting of Exercise We are supposing that the proportion of all adults p.ho think that two children is ideal is p = What is the probability that a sample proportion ˆp falls between 0.46 and 0.52 (that is, within ±3 percentage points of the true p) if the sample is an SRS of size n = 300? Of size n = 5000? Combine these results with your work in Exercise 5.22 to make a general statement about the effect of larger samples in a sample survey. Size n = 300 Crunch it. P(0.46 ˆp 0.52) = P(0.52(300) X 0.46(300)) = P(X 156) P(X 138) = binomdist(156, 300, 0.49, true) binomdist(137, 300, 0.49, true) = = see answer to problem 5.22 for pictorial representation. Normal Approximation. P(0.46 ˆp 0.52) = P(0.52(300) X 0.46(300)) = P(X 156) P(X 138) (0.49) P Z  P 300 Z (0.49) 300 or if using phats PZ (0.49) PZ (0.49) 300 P(Z < 1.039)  P(Z < ) Normal Approximation, continuity correction. P(0.46 ˆp 0.52) = P(0.52(300) X 0.46(300)) = P(X 156) P(X 138) (0.49) P Z  P 300 Z (0.49) 300 P(Z < 1.097)  P(Z < )
5 Size n = 5000 Normal Approximation. P(0.46 ˆp 0.52) = P(0.52(5000) X 0.46(5000)) = P(X 2600) P(X 2300) (0.49) P Z  P 5000 Z (0.49) 5000 P(Z < 4.24)  P(Z < 4.24) P(0.46 ˆp 0.52) = P(0.46(5000) X 0.52(5000)) = P(X 2600) P(X 2300) =binomdist(2600, 5000, 0.49,true) binomdist(2299, 5000, 0.49, true) = Admitting students to college. A selective college would like to have an entering class of 950 students. Because not all students who are offered admission accept, the college admits more than 950 students. Past experience shows that about 75% of the students admitted will accept. The college decides to admit 1200 students. Assuming that students make their decisions independently, the number who accept has the B(1200, 0.75) distribution. If this number is less than 950, the college will admit students from its waiting list. (a) What are the mean and the standard deviation of the number X of students who accept? Notice that we want the mean and standard deviation of the count: of the number X of students who accept? µ X = 1200(0.75) = 900 σ X = 1200(0.75)(0.25) = 15 (b) The college does not want more than 950 students. What is the probability that more than 950 will accept? P(X 951) = = 1 binomdist(950, 1200,0.75,true) Normal Approximation. 1200(0.75) = and 1200(0.25) = (0.75) 1200(0.75)(0.25) P(Z > 3.4)
6 Normal Approximation with continuity correction. 1200(0.75) = and 1200(0.25) = (0.75) 1200(0.75)(0.25) P(Z > 3.37) 1 normsdist(3.37) (c) If the college decides to increase the number of admission offers to 1300, what is the probability that more than 950 will accept? P(X 951) = = 1 binomdist(950,1300,0.75,true) Normal Approximation. 1300(0.75) = and 1300(0.25) = (0.75) 1300(0.75)(0.25) P(Z > ) Normal Approximation with continuity correction. 1300(0.75) = and 1300(0.25) = (0.75) 1300(0.75)(0.25) P(Z > )
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 5.1 Homework Answers 5.7 In the proofreading setting if Exercise 5.3, what is the smallest number of misses m with P(X m)
More informationChapter 7  Practice Problems 1
Chapter 7  Practice Problems 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Define a point estimate. What is the
More informationLecture 10: Depicting Sampling Distributions of a Sample Proportion
Lecture 10: Depicting Sampling Distributions of a Sample Proportion Chapter 5: Probability and Sampling Distributions 2/10/12 Lecture 10 1 Sample Proportion 1 is assigned to population members having a
More informationPoint and Interval Estimates
Point and Interval Estimates Suppose we want to estimate a parameter, such as p or µ, based on a finite sample of data. There are two main methods: 1. Point estimate: Summarize the sample by a single number
More informationChapter 5: Normal Probability Distributions  Solutions
Chapter 5: Normal Probability Distributions  Solutions Note: All areas and zscores are approximate. Your answers may vary slightly. 5.2 Normal Distributions: Finding Probabilities If you are given that
More informationMAT 155. Key Concept. September 27, 2010. 155S5.5_3 Poisson Probability Distributions. Chapter 5 Probability Distributions
MAT 155 Dr. Claude Moore Cape Fear Community College Chapter 5 Probability Distributions 5 1 Review and Preview 5 2 Random Variables 5 3 Binomial Probability Distributions 5 4 Mean, Variance and Standard
More informationPractice problems for Homework 12  confidence intervals and hypothesis testing. Open the Homework Assignment 12 and solve the problems.
Practice problems for Homework 1  confidence intervals and hypothesis testing. Read sections 10..3 and 10.3 of the text. Solve the practice problems below. Open the Homework Assignment 1 and solve the
More informationBinomial random variables
Binomial and Poisson Random Variables Solutions STATUB.0103 Statistics for Business Control and Regression Models Binomial random variables 1. A certain coin has a 5% of landing heads, and a 75% chance
More informationIntroduction to the Practice of Statistics Sixth Edition Moore, McCabe
Introduction to the Practice of Statistics Sixth Edition Moore, McCabe Section 5.1 Homework Answers 5.9 What is wrong? Explain what is wrong in each of the following scenarios. (a) If you toss a fair coin
More informationSOLUTIONS: 4.1 Probability Distributions and 4.2 Binomial Distributions
SOLUTIONS: 4.1 Probability Distributions and 4.2 Binomial Distributions 1. The following table contains a probability distribution for a random variable X. a. Find the expected value (mean) of X. x 1 2
More informationChapter 4. iclicker Question 4.4 Prelecture. Part 2. Binomial Distribution. J.C. Wang. iclicker Question 4.4 Prelecture
Chapter 4 Part 2. Binomial Distribution J.C. Wang iclicker Question 4.4 Prelecture iclicker Question 4.4 Prelecture Outline Computing Binomial Probabilities Properties of a Binomial Distribution Computing
More informationImportant Probability Distributions OPRE 6301
Important Probability Distributions OPRE 6301 Important Distributions... Certain probability distributions occur with such regularity in reallife applications that they have been given their own names.
More information4. Continuous Random Variables, the Pareto and Normal Distributions
4. Continuous Random Variables, the Pareto and Normal Distributions A continuous random variable X can take any value in a given range (e.g. height, weight, age). The distribution of a continuous random
More informationThe normal approximation to the binomial
The normal approximation to the binomial The binomial probability function is not useful for calculating probabilities when the number of trials n is large, as it involves multiplying a potentially very
More informationof course the mean is p. That is just saying the average sample would have 82% answering
Sampling Distribution for a Proportion Start with a population, adult Americans and a binary variable, whether they believe in God. The key parameter is the population proportion p. In this case let us
More informationNormal Distribution as an Approximation to the Binomial Distribution
Chapter 1 Student Lecture Notes 11 Normal Distribution as an Approximation to the Binomial Distribution : Goals ONE TWO THREE 2 Review Binomial Probability Distribution applies to a discrete random variable
More informationChapter 4. Probability Distributions
Chapter 4 Probability Distributions Lesson 41/42 Random Variable Probability Distributions This chapter will deal the construction of probability distribution. By combining the methods of descriptive
More informationProbability Distributions
CHAPTER 5 Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Probability Distribution 5.3 The Binomial Distribution
More informationMATH 214 (NOTES) Math 214 Al Nosedal. Department of Mathematics Indiana University of Pennsylvania. MATH 214 (NOTES) p. 1/6
MATH 214 (NOTES) Math 214 Al Nosedal Department of Mathematics Indiana University of Pennsylvania MATH 214 (NOTES) p. 1/6 "Pepsi" problem A market research consultant hired by the PepsiCola Co. is interested
More informationBinomial random variables (Review)
Poisson / Empirical Rule Approximations / Hypergeometric Solutions STATUB.3 Statistics for Business Control and Regression Models Binomial random variables (Review. Suppose that you are rolling a die
More informationThe normal approximation to the binomial
The normal approximation to the binomial In order for a continuous distribution (like the normal) to be used to approximate a discrete one (like the binomial), a continuity correction should be used. There
More information39.2. The Normal Approximation to the Binomial Distribution. Introduction. Prerequisites. Learning Outcomes
The Normal Approximation to the Binomial Distribution 39.2 Introduction We have already seen that the Poisson distribution can be used to approximate the binomial distribution for large values of n and
More informationAn Introduction to Basic Statistics and Probability
An Introduction to Basic Statistics and Probability Shenek Heyward NCSU An Introduction to Basic Statistics and Probability p. 1/4 Outline Basic probability concepts Conditional probability Discrete Random
More informationIntroduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 4.4 Homework
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 4.4 Homework 4.65 You buy a hot stock for $1000. The stock either gains 30% or loses 25% each day, each with probability.
More information6. Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8? A) (0.6) (0.4) B) 8! C) 45(0.6) (0.
Name: Date:. For each of the following scenarios, determine the appropriate distribution for the random variable X. A) A fair die is rolled seven times. Let X = the number of times we see an even number.
More informationLesson 20. Probability and Cumulative Distribution Functions
Lesson 20 Probability and Cumulative Distribution Functions Recall If p(x) is a density function for some characteristic of a population, then Recall If p(x) is a density function for some characteristic
More informationExperimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test
Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely
More informationJoint Exam 1/P Sample Exam 1
Joint Exam 1/P Sample Exam 1 Take this practice exam under strict exam conditions: Set a timer for 3 hours; Do not stop the timer for restroom breaks; Do not look at your notes. If you believe a question
More informationChapter 8 Section 1. Homework A
Chapter 8 Section 1 Homework A 8.7 Can we use the largesample confidence interval? In each of the following circumstances state whether you would use the largesample confidence interval. The variable
More informationKey Concept. Density Curve
MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 6 Normal Probability Distributions 6 1 Review and Preview 6 2 The Standard Normal Distribution 6 3 Applications of Normal
More informationMath 251, Review Questions for Test 3 Rough Answers
Math 251, Review Questions for Test 3 Rough Answers 1. (Review of some terminology from Section 7.1) In a state with 459,341 voters, a poll of 2300 voters finds that 45 percent support the Republican candidate,
More informationBinomial Distribution Problems. Binomial Distribution SOLUTIONS. Poisson Distribution Problems
1 Binomial Distribution Problems (1) A company owns 400 laptops. Each laptop has an 8% probability of not working. You randomly select 20 laptops for your salespeople. (a) What is the likelihood that 5
More informationReview. March 21, 2011. 155S7.1 2_3 Estimating a Population Proportion. Chapter 7 Estimates and Sample Sizes. Test 2 (Chapters 4, 5, & 6) Results
MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 7 Estimates and Sample Sizes 7 1 Review and Preview 7 2 Estimating a Population Proportion 7 3 Estimating a Population
More information5.1 Identifying the Target Parameter
University of California, Davis Department of Statistics Summer Session II Statistics 13 August 20, 2012 Date of latest update: August 20 Lecture 5: Estimation with Confidence intervals 5.1 Identifying
More informationConfidence Intervals for the Difference Between Two Means
Chapter 47 Confidence Intervals for the Difference Between Two Means Introduction This procedure calculates the sample size necessary to achieve a specified distance from the difference in sample means
More information16. THE NORMAL APPROXIMATION TO THE BINOMIAL DISTRIBUTION
6. THE NORMAL APPROXIMATION TO THE BINOMIAL DISTRIBUTION It is sometimes difficult to directly compute probabilities for a binomial (n, p) random variable, X. We need a different table for each value of
More informationReview #2. Statistics
Review #2 Statistics Find the mean of the given probability distribution. 1) x P(x) 0 0.19 1 0.37 2 0.16 3 0.26 4 0.02 A) 1.64 B) 1.45 C) 1.55 D) 1.74 2) The number of golf balls ordered by customers of
More information3.4 Statistical inference for 2 populations based on two samples
3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted
More informationSTAT 315: HOW TO CHOOSE A DISTRIBUTION FOR A RANDOM VARIABLE
STAT 315: HOW TO CHOOSE A DISTRIBUTION FOR A RANDOM VARIABLE TROY BUTLER 1. Random variables and distributions We are often presented with descriptions of problems involving some level of uncertainty about
More informationCHAPTER 7 SECTION 5: RANDOM VARIABLES AND DISCRETE PROBABILITY DISTRIBUTIONS
CHAPTER 7 SECTION 5: RANDOM VARIABLES AND DISCRETE PROBABILITY DISTRIBUTIONS TRUE/FALSE 235. The Poisson probability distribution is a continuous probability distribution. F 236. In a Poisson distribution,
More informationFrom the standard normal probability table, the answer is approximately 0.89.
!"#$ Find the value z such that P(Z z) = 0.813. From the standard normal probability table, the answer is approximately 0.89. Suppose the running time of a type of machine is known to be a normal random
More informationWeek 3&4: Z tables and the Sampling Distribution of X
Week 3&4: Z tables and the Sampling Distribution of X 2 / 36 The Standard Normal Distribution, or Z Distribution, is the distribution of a random variable, Z N(0, 1 2 ). The distribution of any other normal
More informationCHAPTER 6: Continuous Uniform Distribution: 6.1. Definition: The density function of the continuous random variable X on the interval [A, B] is.
Some Continuous Probability Distributions CHAPTER 6: Continuous Uniform Distribution: 6. Definition: The density function of the continuous random variable X on the interval [A, B] is B A A x B f(x; A,
More informationMathematics and Statistics: Apply probability methods in solving problems (91267)
NCEA Level 2 Mathematics (91267) 2013 page 1 of 5 Assessment Schedule 2013 Mathematics and Statistics: Apply probability methods in solving problems (91267) Evidence Statement with Merit Apply probability
More informationSample Questions for Mastery #5
Name: Class: Date: Sample Questions for Mastery #5 Multiple Choice Identify the choice that best completes the statement or answers the question.. For which of the following binomial experiments could
More informationCh. 6.1 #749 odd. The area is found by looking up z= 0.75 in Table E and subtracting 0.5. Area = 0.77340.5= 0.2734
Ch. 6.1 #749 odd The area is found by looking up z= 0.75 in Table E and subtracting 0.5. Area = 0.77340.5= 0.2734 The area is found by looking up z= 2.07 in Table E and subtracting from 0.5. Area = 0.50.0192
More informationBA 275 Review Problems  Week 5 (10/23/0610/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380394
BA 275 Review Problems  Week 5 (10/23/0610/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380394 1. Does vigorous exercise affect concentration? In general, the time needed for people to complete
More informationECE302 Spring 2006 HW4 Solutions February 6, 2006 1
ECE302 Spring 2006 HW4 Solutions February 6, 2006 1 Solutions to HW4 Note: Most of these solutions were generated by R. D. Yates and D. J. Goodman, the authors of our textbook. I have added comments in
More information1) What is the probability that the random variable has a value greater than 2? A) 0.750 B) 0.625 C) 0.875 D) 0.700
Practice for Chapter 6 & 7 Math 227 This is merely an aid to help you study. The actual exam is not multiple choice nor is it limited to these types of questions. Using the following uniform density curve,
More informationThe Normal Distribution. Alan T. Arnholt Department of Mathematical Sciences Appalachian State University
The Normal Distribution Alan T. Arnholt Department of Mathematical Sciences Appalachian State University arnholt@math.appstate.edu Spring 2006 R Notes 1 Copyright c 2006 Alan T. Arnholt 2 Continuous Random
More informationIntroduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 8.1 Homework Answers
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 8.1 Homework Answers 8.1 In each of the following circumstances state whether you would use the large sample confidence interval,
More informationSampling Distribution of a Sample Proportion
Sampling Distribution of a Sample Proportion From earlier material remember that if X is the count of successes in a sample of n trials of a binomial random variable then the proportion of success is given
More informationCharacteristics of Binomial Distributions
Lesson2 Characteristics of Binomial Distributions In the last lesson, you constructed several binomial distributions, observed their shapes, and estimated their means and standard deviations. In Investigation
More informationThe Math. P (x) = 5! = 1 2 3 4 5 = 120.
The Math Suppose there are n experiments, and the probability that someone gets the right answer on any given experiment is p. So in the first example above, n = 5 and p = 0.2. Let X be the number of correct
More informationSummary of Formulas and Concepts. Descriptive Statistics (Ch. 14)
Summary of Formulas and Concepts Descriptive Statistics (Ch. 14) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume
More informationProbability Distributions
Learning Objectives Probability Distributions Section 1: How Can We Summarize Possible Outcomes and Their Probabilities? 1. Random variable 2. Probability distributions for discrete random variables 3.
More informationChapter 7 Section 1 Homework Set A
Chapter 7 Section 1 Homework Set A 7.15 Finding the critical value t *. What critical value t * from Table D (use software, go to the web and type t distribution applet) should be used to calculate the
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
STT315 Practice Ch 57 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed
More informationThe Binomial Probability Distribution
The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015 Objectives After this lesson we will be able to: determine whether a probability
More informationLecture 5 : The Poisson Distribution
Lecture 5 : The Poisson Distribution Jonathan Marchini November 10, 2008 1 Introduction Many experimental situations occur in which we observe the counts of events within a set unit of time, area, volume,
More informationLecture 13 More on hypothesis testing
Lecture 13 More on hypothesis testing Thais Paiva STA 111  Summer 2013 Term II July 22, 2013 1 / 27 Thais Paiva STA 111  Summer 2013 Term II Lecture 13, 07/22/2013 Lecture Plan 1 Type I and type II error
More information5. Continuous Random Variables
5. Continuous Random Variables Continuous random variables can take any value in an interval. They are used to model physical characteristics such as time, length, position, etc. Examples (i) Let X be
More informationExample 1: Dear Abby. Stat Camp for the Fulltime MBA Program
Stat Camp for the Fulltime MBA Program Daniel Solow Lecture 4 The Normal Distribution and the Central Limit Theorem 188 Example 1: Dear Abby You wrote that a woman is pregnant for 266 days. Who said so?
More informationMath 151. Rumbos Spring 2014 1. Solutions to Assignment #22
Math 151. Rumbos Spring 2014 1 Solutions to Assignment #22 1. An experiment consists of rolling a die 81 times and computing the average of the numbers on the top face of the die. Estimate the probability
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) ±1.88 B) ±1.645 C) ±1.96 D) ±2.
Ch. 6 Confidence Intervals 6.1 Confidence Intervals for the Mean (Large Samples) 1 Find a Critical Value 1) Find the critical value zc that corresponds to a 94% confidence level. A) ±1.88 B) ±1.645 C)
More informationExample 1. so the Binomial Distrubtion can be considered normal
Chapter 6 8B: Examples of Using a Normal Distribution to Approximate a Binomial Probability Distribution Example 1 The probability of having a boy in any single birth is 50%. Use a normal distribution
More informationStats on the TI 83 and TI 84 Calculator
Stats on the TI 83 and TI 84 Calculator Entering the sample values STAT button Left bracket { Right bracket } Store (STO) List L1 Comma Enter Example: Sample data are {5, 10, 15, 20} 1. Press 2 ND and
More informationBowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition
Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology StepbyStep  Excel Microsoft Excel is a spreadsheet software application
More informationNormal distribution. ) 2 /2σ. 2π σ
Normal distribution The normal distribution is the most widely known and used of all distributions. Because the normal distribution approximates many natural phenomena so well, it has developed into a
More informationAP Statistics 7!3! 6!
Lesson 64 Introduction to Binomial Distributions Factorials 3!= Definition: n! = n( n 1)( n 2)...(3)(2)(1), n 0 Note: 0! = 1 (by definition) Ex. #1 Evaluate: a) 5! b) 3!(4!) c) 7!3! 6! d) 22! 21! 20!
More informationMind on Statistics. Chapter 8
Mind on Statistics Chapter 8 Sections 8.18.2 Questions 1 to 4: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. 1. Random variable
More information6.2 Normal distribution. Standard Normal Distribution:
6.2 Normal distribution Slide Heights of Adult Men and Women Slide 2 Area= Mean = µ Standard Deviation = σ Donation: X ~ N(µ,σ 2 ) Standard Normal Distribution: Slide 3 Slide 4 a normal probability distribution
More informationHomework 5 Solutions
Math 130 Assignment Chapter 18: 6, 10, 38 Chapter 19: 4, 6, 8, 10, 14, 16, 40 Chapter 20: 2, 4, 9 Chapter 18 Homework 5 Solutions 18.6] M&M s. The candy company claims that 10% of the M&M s it produces
More informationChapter Five: Paired Samples Methods 1/38
Chapter Five: Paired Samples Methods 1/38 5.1 Introduction 2/38 Introduction Paired data arise with some frequency in a variety of research contexts. Patients might have a particular type of laser surgery
More information6.1. Construct and Interpret Binomial Distributions. p Study probability distributions. Goal VOCABULARY. Your Notes.
6.1 Georgia Performance Standard(s) MM3D1 Your Notes Construct and Interpret Binomial Distributions Goal p Study probability distributions. VOCABULARY Random variable Discrete random variable Continuous
More informationSTA 130 (Winter 2016): An Introduction to Statistical Reasoning and Data Science
STA 130 (Winter 2016): An Introduction to Statistical Reasoning and Data Science Mondays 2:10 4:00 (GB 220) and Wednesdays 2:10 4:00 (various) Jeffrey Rosenthal Professor of Statistics, University of Toronto
More informationPart I Learning about SPSS
STATS 1000 / STATS 1004 / STATS 1504 Statistical Practice 1 Practical Week 5 2015 Practical Outline In this practical, we will look at how to do binomial calculations in Excel. look at how to do normal
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Regular smoker
Exam Chapters 4&5 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) A 28yearold man pays $181 for a oneyear
More informationMath 108 Exam 3 Solutions Spring 00
Math 108 Exam 3 Solutions Spring 00 1. An ecologist studying acid rain takes measurements of the ph in 12 randomly selected Adirondack lakes. The results are as follows: 3.0 6.5 5.0 4.2 5.5 4.7 3.4 6.8
More informationChapter 7  Practice Problems 2
Chapter 7  Practice Problems 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the requested value. 1) A researcher for a car insurance company
More informationIn the general population of 0 to 4yearolds, the annual incidence of asthma is 1.4%
Hypothesis Testing for a Proportion Example: We are interested in the probability of developing asthma over a given oneyear period for children 0 to 4 years of age whose mothers smoke in the home In the
More informationStatistics 104: Section 6!
Page 1 Statistics 104: Section 6! TF: Deirdre (say: Deardra) Bloome Email: dbloome@fas.harvard.edu Section Times Thursday 2pm3pm in SC 109, Thursday 5pm6pm in SC 705 Office Hours: Thursday 6pm7pm SC
More informationDepartment of Civil EngineeringI.I.T. Delhi CEL 899: Environmental Risk Assessment Statistics and Probability Example Part 1
Department of Civil EngineeringI.I.T. Delhi CEL 899: Environmental Risk Assessment Statistics and Probability Example Part Note: Assume missing data (if any) and mention the same. Q. Suppose X has a normal
More informationSection 12.2, Lesson 3. What Can Go Wrong in Hypothesis Testing: The Two Types of Errors and Their Probabilities
Today: Section 2.2, Lesson 3: What can go wrong with hypothesis testing Section 2.4: Hypothesis tests for difference in two proportions ANNOUNCEMENTS: No discussion today. Check your grades on eee and
More informationMath 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2
Math 58. Rumbos Fall 2008 1 Solutions to Review Problems for Exam 2 1. For each of the following scenarios, determine whether the binomial distribution is the appropriate distribution for the random variable
More informationStatistics 100 Binomial and Normal Random Variables
Statistics 100 Binomial and Normal Random Variables Three different random variables with common characteristics: 1. Flip a fair coin 10 times. Let X = number of heads out of 10 flips. 2. Poll a random
More informationChicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011
Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this
More informationChapter 3: DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
Chapter 3: DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS Part 4: Geometric Distribution Negative Binomial Distribution Hypergeometric Distribution Sections 37, 38 The remaining discrete random
More informationLecture 8 Hypothesis Testing
Lecture 8 Hypothesis Testing Fall 2013 Prof. Yao Xie, yao.xie@isye.gatech.edu H. Milton Stewart School of Industrial Systems & Engineering Georgia Tech Midterm 1 Score 46 students Highest score: 98 Lowest
More informationStatistics 100A Homework 4 Solutions
Problem 1 For a discrete random variable X, Statistics 100A Homework 4 Solutions Ryan Rosario Note that all of the problems below as you to prove the statement. We are proving the properties of epectation
More informationStatistics 100A Homework 7 Solutions
Chapter 6 Statistics A Homework 7 Solutions Ryan Rosario. A television store owner figures that 45 percent of the customers entering his store will purchase an ordinary television set, 5 percent will purchase
More informationNormal Approximation. Contents. 1 Normal Approximation. 1.1 Introduction. Anthony Tanbakuchi Department of Mathematics Pima Community College
Introductory Statistics Lectures Normal Approimation To the binomial distribution Department of Mathematics Pima Community College Redistribution of this material is prohibited without written permission
More informationLesson 17: Margin of Error When Estimating a Population Proportion
Margin of Error When Estimating a Population Proportion Classwork In this lesson, you will find and interpret the standard deviation of a simulated distribution for a sample proportion and use this information
More informationConfidence Intervals (Review)
Intro to Hypothesis Tests Solutions STATUB.0103 Statistics for Business Control and Regression Models Confidence Intervals (Review) 1. Each year, construction contractors and equipment distributors from
More informationb. What is the probability of an event that is certain to occur? ANSWER: P(certain to occur) = 1.0
MTH 157 Sample Test 2 ANSWERS Student Row Seat M157ST2a Chapters 3 & 4 Dr. Claude S. Moore Score SHOW ALL NECESSARY WORK. Be Neat and Organized. Good Luck. 1. In a statistics class, 12 students own their
More informationName: Date: Use the following to answer questions 34:
Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin
More informationCh5: Discrete Probability Distributions Section 51: Probability Distribution
Recall: Ch5: Discrete Probability Distributions Section 51: Probability Distribution A variable is a characteristic or attribute that can assume different values. o Various letters of the alphabet (e.g.
More informationAP STATISTICS (WarmUp Exercises)
AP STATISTICS (WarmUp Exercises) 1. Describe the distribution of ages in a city: 2. Graph a box plot on your calculator for the following test scores: {90, 80, 96, 54, 80, 95, 100, 75, 87, 62, 65, 85,
More informationIntroduction to the Practice of Statistics Fifth Edition Moore, McCabe
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 1.3 Homework Answers 1.80 If you ask a computer to generate "random numbers between 0 and 1, you uniform will get observations
More informationDETERMINE whether the conditions for a binomial setting are met. COMPUTE and INTERPRET probabilities involving binomial random variables
1 Section 7.B Learning Objectives After this section, you should be able to DETERMINE whether the conditions for a binomial setting are met COMPUTE and INTERPRET probabilities involving binomial random
More information