9.2 Examples. Example 1
|
|
- Natalie George
- 7 years ago
- Views:
Transcription
1 9.2 Examples Example 1 A simple random sample of size n is drawn. The sample mean,, is found to be 19.2, and the sample standard deviation, s, is found to be 4.7. a) Construct a 95% confidence interval about µ (population mean) if the sample size, n, is 35. READ pages However, we will use our calculator!! On your calculator, Go to STAT, then TESTS, then scroll down to TInterval. You will have a choice of data or stats. We will choose stats since we know the mean and standard deviation, rather than having a list of data values. gives you this: So the interval, rounded to two decimal places, is (17.59, 20.82) b) Construct a 95% confidence interval about µ (population mean) if the sample size, n, is 51. gives you this: So the interval, rounded to two decimal places, is (17.88, 20.52)
2 How does increasing the sample size affect the margin of error, E? Since you are DIVIDING by the square root of n, as n (the sample size) gets larger, it will cause this value to decrease. (Dividing by a larger number gives you a smaller answer!) So, the margin of error decreases as n gets larger. c) Construct a 99% confidence interval about µ (population mean) if the sample size, n, is 35. gives you this: So the interval, rounded to two decimal places, is (17.03, 21.37) d) If the sample size is 16, what conditions must be satisfied to compute the confidence interval? Example 2 A trade magazine routinely checks the drive-through service times of fast-food restaurants. A 90% confidence interval that results from examining 519 customers in one fast food chain s drive-through has a lower bound of seconds and an upper bound of seconds. What does this mean? One can be 90% confident that the mean drive-through service time of this chain is between and seconds.
3 Example 3 In a survey conducted by a polling company, 1100 adult Americans were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean numbers of hours worked had a lower boung of 42.7 and an upper bound of Provide two recommendations for increasing the precision of the interval. **Decrease the confidence level. **Increase the sample size. (Read pages ) Example 4 A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 960 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.62 hours with a standard deviation of 0.65 hour. a) A histogram of time spent eating/drinking each day is skewed right. Use this result to explain why a large sample is needed to construct a confidence interval for the mean. *Since the distribution is skewed right (not normally distributed) the sample must be large so that the distribution of the same mean will be approximately normal. b) In 2010, there were over 200 million people nationally age 15 or older. Explain why this, along with the fact that our data is from a random sample, satisfies the requirements for constructing a confidence interval. *The sample size is less than 5% of the population (n < 0.05N) c) Determine and interpret a 95% confidence interval for the mean amount of time Americans age 15 or older spend eating/drinking each day. gives us this: Rounded to two places, the interval is (1.58, 1.66) Which means the nutritionist can be 95% confident that the mean amount of time Americans spend eating/drinking per day is between 1.58 and 1.66 hours.
4 d) Could this interval be used to estimate the mean amount of time a 9-year-old spends eating and drinking per day? *No, the interval is about people age 15 and older. The amount for 9-year-olds could easily be very different. Example 5 A poll conducted in 1970 asked 1007 people, During the past year, about how many books, either hardcover or paperback, did you read either all or part of the way through? Results of this survey indicated that = 18.9 books and s = 19.9 books. a) Construct a 95% confidence interval for the mean number of books read all or part of the way through during the preceding year and interpret it. gives you this: Rounded to two places, the interval is (17.67, 20.13) So we are 95% confident that the mean number of books read is between and b) Compare these results to a recent survey of 1007 people. The results indicated that = 12.7 books and s = 15.9 books. A 95% confidence interval for this survey is (11.72, 13.68). Were people reading more in 1970 than they are today? *Yes. We are 95% confident that the mean number of books read is between and instead of and This is a decrease. Example 6 The trade volume of a stock is the number of shares traded on a given day. The following data, in millions (so that 2.45 represents 2,450,000 shares), represent the volume of a certain stock traded for a random sample of 40 trading days in 2007.
5 a) Use this data to compute a point estimate for the population mean number of shares traded per day in Enter this data into L1 in your calculator. and so on... 1-var stats gives you = (rounded to three places) And also note that s = b) Construct a 90% confidence interval for the population mean number of shares traded per day in gives you this: So the interval rounded to three places is (2.014, 2.662) So there is a 90% confidence that the mean number of shares of the stock traded per day in 2007 is btween 2,014,000 and 2,662,000. c) A second random sample of 40 days in 2007 resulted in the following data. Construct a 90% confidence interval for the population mean number of shares traded per day in 2007.
6 Follow the same steps as in part b above. Enter this data into L1, find the 1-var stats to determine and s so that you can do the TInterval on your calculator. This interval you should obtain is (2.248, 3.111). The two confidence intervals are different because of variation in sampling. The samples have different means and standard deviations that lead to different confidence intervals. Example 7 People were polled on how many books they read the previous year. Initial survey results indicate that s = 11.2 books. a) How many subjects are needed to estimate the number of books read the previous year within six books with 90% confidence? E = 6 ( within 6 books ) The critical value z α/2 that corresponds to 90% confidence is (see page 395) n = [(1.645*11.2)/6] 2 = = (we always round up because we are talking about a minimum sample size) Therefore the 90% confidence level requires 10 subjects. b) How many subjects are needed to estimate the number of books read the previous year within three books with 90% confidence?
7 E = 3 ( within 3 books ) The critical value z α/2 that corresponds to 90% confidence is (see page 395) n = [(1.645*11.2)/3] 2 = = (we always round up because we are talking about a minimum sample size) Therefore the 90% confidence level requires 38 subjects. c) What effect does doubling the required accuracy have on the sample size? Doubling the required accuracy quadruples the required sample size. (A sample size 38 is almost 4 times larger than a sample size of 10. Increasing the accuracy needed will always increase the sample size needed. ) d) How many subjects are needed to estimate the number of books read the previous year within six books with 99% confidence? E = 6 ( within 6 books ) The critical value z α/2 that corresponds to 99% confidence is (see page 395) n = [ (2.575*11.2)/6] 2 = = (we always round up because we are talking about a minimum sample size) Therefore the 99% confidence level requires 24 subjects. Compare this result to part (a). How does the increasing level of confidence in the estimate affect sample size? Why is this reasonable? Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size.
8 Enter the data into L1, L2, L3 on your calculator. Example 8
9 = Sx = n = 8 = Sx = n = 20 = 99.2 Sx = n = 30 b) answer: (83.73, )
10 answer: (91.88, ) answer: (93.70, 104.7)
Point 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 informationConfidence Intervals
Section 6.1 75 Confidence Intervals Section 6.1 C H A P T E R 6 4 Example 4 (pg. 284) Constructing a Confidence Interval Enter the data from Example 1 on pg. 280 into L1. In this example, n > 0, so the
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 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 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 informationWeek 4: Standard Error and Confidence Intervals
Health Sciences M.Sc. Programme Applied Biostatistics Week 4: Standard Error and Confidence Intervals Sampling Most research data come from subjects we think of as samples drawn from a larger population.
More informationSAMPLING DISTRIBUTIONS
0009T_c07_308-352.qd 06/03/03 20:44 Page 308 7Chapter SAMPLING DISTRIBUTIONS 7.1 Population and Sampling Distributions 7.2 Sampling and Nonsampling Errors 7.3 Mean and Standard Deviation of 7.4 Shape of
More informationp ˆ (sample mean and sample
Chapter 6: Confidence Intervals and Hypothesis Testing When analyzing data, we can t just accept the sample mean or sample proportion as the official mean or proportion. When we estimate the statistics
More informationChapter 7 Review. Confidence Intervals. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Chapter 7 Review Confidence Intervals MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Suppose that you wish to obtain a confidence interval for
More informationc. Construct a boxplot for the data. Write a one sentence interpretation of your graph.
MBA/MIB 5315 Sample Test Problems Page 1 of 1 1. An English survey of 3000 medical records showed that smokers are more inclined to get depressed than non-smokers. Does this imply that smoking causes depression?
More informationMEASURES OF VARIATION
NORMAL DISTRIBTIONS MEASURES OF VARIATION In statistics, it is important to measure the spread of data. A simple way to measure spread is to find the range. But statisticians want to know if the data are
More informationMind on Statistics. Chapter 10
Mind on Statistics Chapter 10 Section 10.1 Questions 1 to 4: Some statistical procedures move from population to sample; some move from sample to population. For each of the following procedures, determine
More informationGood luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:
Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours
More informationMATH 103/GRACEY PRACTICE EXAM/CHAPTERS 2-3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MATH 3/GRACEY PRACTICE EXAM/CHAPTERS 2-3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The frequency distribution
More informationWhat is Statistic? OPRE 6301
What is Statistic? OPRE 6301 In today s world...... we are constantly being bombarded with statistics and statistical information. For example: Customer Surveys Medical News Demographics Political Polls
More informationConfidence Intervals for Cpk
Chapter 297 Confidence Intervals for Cpk Introduction This routine calculates the sample size needed to obtain a specified width of a Cpk confidence interval at a stated confidence level. Cpk is a process
More informationConfidence Intervals for One Standard Deviation Using Standard Deviation
Chapter 640 Confidence Intervals for One Standard Deviation Using Standard Deviation Introduction This routine calculates the sample size necessary to achieve a specified interval width or distance from
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 informationConfidence Intervals for Cp
Chapter 296 Confidence Intervals for Cp Introduction This routine calculates the sample size needed to obtain a specified width of a Cp confidence interval at a stated confidence level. Cp is a process
More informationThe right edge of the box is the third quartile, Q 3, which is the median of the data values above the median. Maximum Median
CONDENSED LESSON 2.1 Box Plots In this lesson you will create and interpret box plots for sets of data use the interquartile range (IQR) to identify potential outliers and graph them on a modified box
More informationChapter Study Guide. Chapter 11 Confidence Intervals and Hypothesis Testing for Means
OPRE504 Chapter Study Guide Chapter 11 Confidence Intervals and Hypothesis Testing for Means I. Calculate Probability for A Sample Mean When Population σ Is Known 1. First of all, we need to find out the
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 informationUnit 26 Estimation with Confidence Intervals
Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference
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 informationObjective To introduce the concept of square roots and the use of the square-root key on a calculator. Assessment Management
Unsquaring Numbers Objective To introduce the concept of square roots and the use of the square-root key on a calculator. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts
More information5/31/2013. 6.1 Normal Distributions. Normal Distributions. Chapter 6. Distribution. The Normal Distribution. Outline. Objectives.
The Normal Distribution C H 6A P T E R The Normal Distribution Outline 6 1 6 2 Applications of the Normal Distribution 6 3 The Central Limit Theorem 6 4 The Normal Approximation to the Binomial Distribution
More informationData Analysis Tools. Tools for Summarizing Data
Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool
More informationStandard Deviation Estimator
CSS.com Chapter 905 Standard Deviation Estimator Introduction Even though it is not of primary interest, an estimate of the standard deviation (SD) is needed when calculating the power or sample size of
More informationMeans, standard deviations and. and standard errors
CHAPTER 4 Means, standard deviations and standard errors 4.1 Introduction Change of units 4.2 Mean, median and mode Coefficient of variation 4.3 Measures of variation 4.4 Calculating the mean and standard
More informationDensity Curve. A density curve is the graph of a continuous probability distribution. It must satisfy the following properties:
Density Curve A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: 1. The total area under the curve must equal 1. 2. Every point on the curve
More informationHow to Verify Performance Specifications
How to Verify Performance Specifications VERIFICATION OF PERFORMANCE SPECIFICATIONS In 2003, the Centers for Medicare and Medicaid Services (CMS) updated the CLIA 88 regulations. As a result of the updated
More informationCalculation example mean, median, midrange, mode, variance, and standard deviation for raw and grouped data
Calculation example mean, median, midrange, mode, variance, and standard deviation for raw and grouped data Raw data: 7, 8, 6, 3, 5, 5, 1, 6, 4, 10 Sorted data: 1, 3, 4, 5, 5, 6, 6, 7, 8, 10 Number of
More informationMBA 611 STATISTICS AND QUANTITATIVE METHODS
MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain
More informationChapter 5 Analysis of variance SPSS Analysis of variance
Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means One-way ANOVA To test the null hypothesis that several population means are equal,
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 informationDef: The standard normal distribution is a normal probability distribution that has a mean of 0 and a standard deviation of 1.
Lecture 6: Chapter 6: Normal Probability Distributions A normal distribution is a continuous probability distribution for a random variable x. The graph of a normal distribution is called the normal curve.
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 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 informationMind on Statistics. Chapter 12
Mind on Statistics Chapter 12 Sections 12.1 Questions 1 to 6: For each statement, determine if the statement is a typical null hypothesis (H 0 ) or alternative hypothesis (H a ). 1. There is no difference
More informationChapter 19 Confidence Intervals for Proportions
Chapter 19 Confidence Intervals for Proportions Use your TI calculator to find the confidence interval. You must know the number of successes, the sample size and confidence level. Under STAT go to TESTS.
More information7.6 Approximation Errors and Simpson's Rule
WileyPLUS: Home Help Contact us Logout Hughes-Hallett, Calculus: Single and Multivariable, 4/e Calculus I, II, and Vector Calculus Reading content Integration 7.1. Integration by Substitution 7.2. Integration
More informationElaboration of Scrum Burndown Charts.
. Combining Control and Burndown Charts and Related Elements Discussion Document By Mark Crowther, Empirical Pragmatic Tester Introduction When following the Scrum approach a tool frequently used is the
More informationGambling participation: activities and mode of access
Gambling participation: activities and mode of access January 2015 1 Key findings 1.1 The following findings are based on a set of questions commissioned by the Gambling Commission in omnibus surveys conducted
More informationYou flip a fair coin four times, what is the probability that you obtain three heads.
Handout 4: Binomial Distribution Reading Assignment: Chapter 5 In the previous handout, we looked at continuous random variables and calculating probabilities and percentiles for those type of variables.
More informationStats Review Chapters 9-10
Stats Review Chapters 9-10 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test
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 informationNumerical Methods for Option Pricing
Chapter 9 Numerical Methods for Option Pricing Equation (8.26) provides a way to evaluate option prices. For some simple options, such as the European call and put options, one can integrate (8.26) directly
More informationCalculating VaR. Capital Market Risk Advisors CMRA
Calculating VaR Capital Market Risk Advisors How is VAR Calculated? Sensitivity Estimate Models - use sensitivity factors such as duration to estimate the change in value of the portfolio to changes in
More informationStatistics 151 Practice Midterm 1 Mike Kowalski
Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and
More informationContinuing, we get (note that unlike the text suggestion, I end the final interval with 95, not 85.
Chapter 3 -- Review Exercises Statistics 1040 -- Dr. McGahagan Problem 1. Histogram of male heights. Shaded area shows percentage of men between 66 and 72 inches in height; this translates as "66 inches
More informationThe Margin of Error for Differences in Polls
The Margin of Error for Differences in Polls Charles H. Franklin University of Wisconsin, Madison October 27, 2002 (Revised, February 9, 2007) The margin of error for a poll is routinely reported. 1 But
More informationMath 201: Statistics November 30, 2006
Math 201: Statistics November 30, 2006 Fall 2006 MidTerm #2 Closed book & notes; only an A4-size formula sheet and a calculator allowed; 90 mins. No questions accepted! Instructions: There are eleven pages
More information2 Sample t-test (unequal sample sizes and unequal variances)
Variations of the t-test: Sample tail Sample t-test (unequal sample sizes and unequal variances) Like the last example, below we have ceramic sherd thickness measurements (in cm) of two samples representing
More informationPremaster Statistics Tutorial 4 Full solutions
Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for
More informationResults of EKOS-CBC MARKETPLACE SURVEY. February 2009
Results of EKOS-CBC MARKETPLACE SURVEY February 9 Methodology This survey was conducted February 12-16, 9 using EKOS unique hybrid internettelephone research panel, Probit. This panel is randomly recruited
More informationCalculator Notes for the TI-Nspire and TI-Nspire CAS
CHAPTER 11 Calculator Notes for the Note 11A: Entering e In any application, press u to display the value e. Press. after you press u to display the value of e without an exponent. Note 11B: Normal Graphs
More information8 6 X 2 Test for a Variance or Standard Deviation
Section 8 6 x 2 Test for a Variance or Standard Deviation 437 This test uses the P-value method. Therefore, it is not necessary to enter a significance level. 1. Select MegaStat>Hypothesis Tests>Proportion
More informationConfidence Intervals for Exponential Reliability
Chapter 408 Confidence Intervals for Exponential Reliability Introduction This routine calculates the number of events needed to obtain a specified width of a confidence interval for the reliability (proportion
More informationCALCULATIONS & STATISTICS
CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents
More informationHow To Calculate Confidence Intervals In A Population Mean
Chapter 8 Confidence Intervals 8.1 Confidence Intervals 1 8.1.1 Student Learning Objectives By the end of this chapter, the student should be able to: Calculate and interpret confidence intervals for one
More informationDescriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics
Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),
More informationConstructing and Interpreting Confidence Intervals
Constructing and Interpreting Confidence Intervals Confidence Intervals In this power point, you will learn: Why confidence intervals are important in evaluation research How to interpret a confidence
More informationAnswers: a. 87.5325 to 92.4675 b. 87.06 to 92.94
1. The average monthly electric bill of a random sample of 256 residents of a city is $90 with a standard deviation of $24. a. Construct a 90% confidence interval for the mean monthly electric bills of
More informationBiostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY
Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY 1. Introduction Besides arriving at an appropriate expression of an average or consensus value for observations of a population, it is important to
More informationSocial Studies 201 Notes for November 19, 2003
1 Social Studies 201 Notes for November 19, 2003 Determining sample size for estimation of a population proportion Section 8.6.2, p. 541. As indicated in the notes for November 17, when sample size is
More informationNCSS Statistical Software
Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, two-sample t-tests, the z-test, the
More informationAccounting Principals Workonomix Survey 2013. March 13, 2013
Accounting Principals Workonomix Survey 2013 March 13, 2013 Survey Background & Methodology Background Accounting Principals polled 1,020 working Americans about the impact of the changes to the payroll
More informationStatistics Review PSY379
Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses
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 informationMind on Statistics. Chapter 2
Mind on Statistics Chapter 2 Sections 2.1 2.3 1. Tallies and cross-tabulations are used to summarize which of these variable types? A. Quantitative B. Mathematical C. Continuous D. Categorical 2. The table
More informationStat 20: Intro to Probability and Statistics
Stat 20: Intro to Probability and Statistics Lecture 16: More Box Models Tessa L. Childers-Day UC Berkeley 22 July 2014 By the end of this lecture... You will be able to: Determine what we expect the sum
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationChapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing
Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing 8-3 Testing a Claim About a Proportion 8-5 Testing a Claim About a Mean: s Not Known 8-6 Testing
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression
More informationScatter Plots with Error Bars
Chapter 165 Scatter Plots with Error Bars Introduction The procedure extends the capability of the basic scatter plot by allowing you to plot the variability in Y and X corresponding to each point. Each
More informationMarks-to-Market in U.S. Treasury Futures and Options: Conventions for Computing Variation Margin Amounts
Marks-to-Market in U.S. Treasury Futures and Options: Conventions for Computing Variation Margin Amounts Treasury futures and options routinely trade at price levels that, in theory, would lead to variation
More informationGetting Started with Statistics. Out of Control! ID: 10137
Out of Control! ID: 10137 By Michele Patrick Time required 35 minutes Activity Overview In this activity, students make XY Line Plots and scatter plots to create run charts and control charts (types of
More informationChapter 23 Inferences About Means
Chapter 23 Inferences About Means Chapter 23 - Inferences About Means 391 Chapter 23 Solutions to Class Examples 1. See Class Example 1. 2. We want to know if the mean battery lifespan exceeds the 300-minute
More informationTI 83/84 Calculator The Basics of Statistical Functions
What you want to do How to start What to do next Put Data in Lists STAT EDIT 1: EDIT ENTER Clear numbers already in a list: Arrow up to L1, then hit CLEAR, ENTER. Then just type the numbers into the appropriate
More informationSample Size Issues for Conjoint Analysis
Chapter 7 Sample Size Issues for Conjoint Analysis I m about to conduct a conjoint analysis study. How large a sample size do I need? What will be the margin of error of my estimates if I use a sample
More informationEXAM #1 (Example) Instructor: Ela Jackiewicz. Relax and good luck!
STP 231 EXAM #1 (Example) Instructor: Ela Jackiewicz Honor Statement: I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned.
More informationAMS 5 CHANCE VARIABILITY
AMS 5 CHANCE VARIABILITY The Law of Averages When tossing a fair coin the chances of tails and heads are the same: 50% and 50%. So if the coin is tossed a large number of times, the number of heads and
More informationDESCRIPTIVE RESEARCH DESIGNS
DESCRIPTIVE RESEARCH DESIGNS Sole Purpose: to describe a behavior or type of subject not to look for any specific relationships, nor to correlate 2 or more variables Disadvantages since setting is completely
More informationProbability and Statistics Prof. Dr. Somesh Kumar Department of Mathematics Indian Institute of Technology, Kharagpur
Probability and Statistics Prof. Dr. Somesh Kumar Department of Mathematics Indian Institute of Technology, Kharagpur Module No. #01 Lecture No. #15 Special Distributions-VI Today, I am going to introduce
More informationHM REVENUE & CUSTOMS. Child and Working Tax Credits. Error and fraud statistics 2008-09
HM REVENUE & CUSTOMS Child and Working Tax Credits Error and fraud statistics 2008-09 Crown Copyright 2010 Estimates of error and fraud in Tax Credits 2008-09 Introduction 1. Child Tax Credit (CTC) and
More informationFinal Exam Practice Problem Answers
Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal
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 information6. Decide which method of data collection you would use to collect data for the study (observational study, experiment, simulation, or survey):
MATH 1040 REVIEW (EXAM I) Chapter 1 1. For the studies described, identify the population, sample, population parameters, and sample statistics: a) The Gallup Organization conducted a poll of 1003 Americans
More informationPhonics. High Frequency Words P.008. Objective The student will read high frequency words.
P.008 Jumping Words Objective The student will read high frequency words. Materials High frequency words (P.HFW.005 - P.HFW.064) Choose target words. Checkerboard and checkers (Activity Master P.008.AM1a
More informationSolutions to Homework Problems for Basic Cost Behavior by David Albrecht
Solutions to Homework Problems for Basic Cost Behavior by David Albrecht Solution to Problem #11 This problem focuses on being able to work with both total cost and average per unit cost. As a brief review,
More informationSeptember 2015. Population analysis of the Retriever (Flat Coated) breed
Population analysis of the Retriever (Flat Coated) breed Genetic analysis of the Kennel Club pedigree records of the UK Retriever (Flat Coated) population has been carried out with the aim of estimating
More informationLecture Notes Module 1
Lecture Notes Module 1 Study Populations A study population is a clearly defined collection of people, animals, plants, or objects. In psychological research, a study population usually consists of a specific
More informationDrawing a histogram using Excel
Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries to
More informationChapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion
Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion Learning Objectives Upon successful completion of Chapter 8, you will be able to: Understand terms. State the null and alternative
More informationThe correlation coefficient
The correlation coefficient Clinical Biostatistics The correlation coefficient Martin Bland Correlation coefficients are used to measure the of the relationship or association between two quantitative
More informationTImath.com. Statistics. Areas in Intervals
Areas in Intervals ID: 9472 TImath.com Time required 30 minutes Activity Overview In this activity, students use several methods to determine the probability of a given normally distributed value being
More informationCoefficient of Determination
Coefficient of Determination The coefficient of determination R 2 (or sometimes r 2 ) is another measure of how well the least squares equation ŷ = b 0 + b 1 x performs as a predictor of y. R 2 is computed
More informationStatistical Process Control (SPC) Training Guide
Statistical Process Control (SPC) Training Guide Rev X05, 09/2013 What is data? Data is factual information (as measurements or statistics) used as a basic for reasoning, discussion or calculation. (Merriam-Webster
More informationProbability Distributions
CHAPTER 6 Probability Distributions Calculator Note 6A: Computing Expected Value, Variance, and Standard Deviation from a Probability Distribution Table Using Lists to Compute Expected Value, Variance,
More information