# Suppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1

Save this PDF as:

Size: px
Start display at page:

Download "Suppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1"

## Transcription

1 AP Statistics: 10.2: Comparing Two Means Name: Suppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1 and µ 2 are the true mean responses for Treatment 1 and Treatment 2, respectively. We use the mean response in the two groups to make the comparison. Using Fathom software, we generated an SRS of 12 girls and a separate SRS of 8 boys and calculated the sample mean heights. The difference in sample means was then calculated and plotted. We repeated this process 1000 times. The results are below The Sampling Distribution of x1 x2 Shape: Normal if both population distributions are Normal; approximately Normal Otherwise if both samples are large enough ( n >= 30) by CLT Center: Its mean is 1 2 Spread: As long as each sample is no more than 10% of its population ( 10% condition), Its standard deviation is n n

2 Refer to the example on P- 631: Who s Taller: Boys or Girls A potato chip manufacturer buys potatoes from two different suppliers, Riderwood Farms and Camberley, Inc. The weights of potatoes from Riderwood Farms are approximately Normally distributed with a mean of 175 grams and a standard deviation of 25 grams. The weights of potatoes from Camberley, Inc. are approximately Normally distributed with a mean of 180 grams and a standard deviation of 30 grams. When shipments arrive at the factory, inspectors randomly select a sample of 20 potatoes from each shipment and weigh them. They are surprised when the average weight of the potatoes in the sample from Riderwood Farms xr was higher than the average weight of the potatoes in the sample from Camberley, Inc. x c. Problem: (a) Describe the shape, center, and spread of the sampling distribution of xc xr. (b) Find the probability that the mean weight of the Riderwood sample is larger than the mean weight of the Camberley sample. Should the inspectors have been surprised? Answers: (a) The shape of the sampling distribution of xc xr is approximately Normal since both population distributions are approximately Normal. The mean of the sampling distribution is = 5 grams and its standard deviation is = (b) If the mean of the Riderwood sample is larger, then xc xr must be negative. The graph below shows the sampling distribution with the desired probability shaded. P( x c x r < 0) = 0 5 Pz 8.73 = P(z < 0.57) = The inspectors shouldn t be surprised since the Riderwood sample with have a higher mean over onefourth of the time.

3 Two- Sample t- Statistic : P- 633 Formula: Standard Error= s n s n Two Practical options for using the two-sample t-procedures. ( P- 633) t (x 1 x 2 ) ( 1 2 ) 1) Technology : Use the t distribution used with degrees of freedom calculated by the data 2) Conservative: Use the t-distribution with df equal to the smaller of n 1 n 2 1, 1 (With this option, the resulting confidence interval has a margin of error as large as or large than is needed for the desired confidence level. The Significance test using this option gives a P-value equal to or greater than the true P- value.) Confidence interval: 2-sample t-interval for a Difference between two Means s 1 2 n 1 s 2 2 n 2 Formula: RECOMMENDATION: USE CALCULATOR

4 Refer to Example on P Do plastic bags from Target or plastic bags from Walmart hold more weight? A group of AP Statistic students decided to investigate by filling a random sample of 5 bags from each store with common grocery items until the bags ripped. Then they weighed the contents of items in each bag to determine its capacity. Here are their results, in grams: Target: 12,572 13,999 11,215 15,447 10,896 Walmart: , Problem: (a) Construct and interpret a 99% confidence interval for the difference in mean capacity of plastic grocery bags from Target and Walmart. (b) Does your interval provide convincing evidence that there is a difference in the mean capacity among the two stores? Walmart Solution: a) State: We want to estimate T W at the 99% confidence level where T = the mean capacity of plastic bags from Target (in grams) and W = the mean capacity of plastic bags from Walmart (in grams). Plan: If the conditions are met, we will calculate a two-sample t interval for T. Random: The students selected a random sample of bags from each store. Normal: Since the sample sizes are small, we must graph the data to see if it is reasonable to assume that the population distributions are approximately Normal. W Since there is no obvious skewness or outliers, it is safe to use t procedures. Independent: The samples were selected independently and it is reasonable to assume that there are more than 10(5) = 50 plastic grocery bags at each store. Do: For these data, x T = , s T = , x = 9234, s = W W Using the conservative df of 5 1 = 4, the critical value for 99% confidence is t* = Thus, the confidence interval is: = = ( 1380, ). With technology and df =7.5, CI = ( 101, 7285). Notice how much narrower this interval is. (2 Sample T Int)

5 Conclude: We are 99% confident that the interval from 1380 to 8564 grams captures the true difference in the mean capacity for plastic grocery bags from Target and from Walmart. (b) Since the interval includes 0, it is plausible that there is no difference in the two means. Thus, we do not have convincing evidence that there is a difference in mean capacity. However, if we increased the sample size we would likely find a convincing difference since it seems pretty clear that Target bags have a bigger capacity. Formula for Degrees of freedom: P- 637 (RECOMMENDATION: USE CALCULATOR) df = s n s n 1 s2 1 s 1 n1 1 n1 n2 1 n2 2 Significance Tests : Two Sample T-Test For The Difference Between Two Means State: H 0 : µ 1 - µ 2 = 0 or( H 0 : µ 1 = µ 2 ) H a : µ 1 - µ 2 > 0, H a : µ 1 - µ 2 < 0, or H a : µ 1 - µ 2 0 Formula:

6 To find the P-value, use the t distribution with degrees of freedom given by technology or by the conservative approach (df = smaller of n 1-1 and n 2-1). Random, Normal, Independent: P- 639 Refer to the Example on P- 640: In commercials for Bounty paper towels, the manufacturer claims that they are the quicker picker-upper. But are they also the stronger picker upper? Two AP Statistics students, Wesley and Maverick, decided to find out. They selected a random sample of 30 Bounty paper towels and a random sample of 30 generic paper towels and measured their strength when wet. To do this, they uniformly soaked each paper towel with 4 ounces of water, held two opposite edges of the paper towel, and counted how many quarters each paper towel could hold until ripping, alternating brands. Here are their results: Bounty: 106, 111, 106, 120, 103, 112, 115, 125, 116, 120, 126, 125, 116, 117, , 126, 120, 115, 116, 121, 113, 111, 128, 124, 125, 127, 123, 115, 114 Generic: 77, 103, 89, 79, 88, 86, 100, 90, 81, 84, 84, 96, 87, 79, 90 86, 88, 81, 91, 94, 90, 89, 85, 83, 89, 84, 90, 100, 94, 87 Problem: (a) Display these distributions using parallel boxplots and briefly compare these distributions. Based only on the boxplots, discuss whether or not you think the mean for Bounty is significantly higher than the mean for generic. (b) Use a significance test to determine if there is convincing evidence that wet Bounty paper towels can hold more weight, on average, than wet generic paper towels. (c) Interpret the P-value from (b) in the context of this question. ( TAKE A DEEP BREATH AND START!!!!!!!!)

7 (a) The five-number summary for the Bounty paper towels is (103, 114, 116.5, 124, 128) and the five-number summary for the generic paper towels is (77, 84, 88, 90, 103). Here are the boxplots: Both distributions are roughly symmetric, but the generic brand has two high outliers. The center of the Bounty distribution is much higher than the center of the generic distribution. Although the range of each distribution is roughly the same, the interquartile range of the Bounty distribution is larger. Since the centers are so far apart and there is almost no overlap in the two distributions, the Bounty mean is almost certain to be significantly higher than the generic mean. If the means were really the same, it would be virtually impossible to get so little overlap. (b) State: We want to perform a test of H 0 : B G = 0 versus H a : B G > 0 at the 5% level of significance where B = the mean number of quarters a wet Bounty paper towel can hold and G = the mean number of quarters a wet generic paper towel can hold. (c) Plan: If the conditions are met, we will conduct a two-sample t test for B G. Random: The students used a random sample of paper towels from each brand. Normal: Even though there were two outliers in the generic distribution, both distributions were reasonably symmetric and the sample sizes are both at least 30, so it is safe to use t procedures. Independent: The samples were selected independently and it is reasonable to assume there are more than 10(30) = 300 paper towels of each brand. Do: For these data, x B = 117.6, s B = 6.64, x = 88.1, and s = G G Test statistic: t = P-value: Using either the conservative df = 30 1 = 29 or from technology (df = 57.8), the P-value is approximately 0. Conclude: Since the P-value is less than 0.05, we reject H 0. There is very convincing evidence that wet Bounty paper towels can hold more weight, on average, than wet generic paper towels. (c) Since the P-value is approximately 0, it is almost impossible to get a difference in means of at least 29.5 quarters by random chance, assuming that the two brands of paper towels can hold the same amount of weight when wet.

8 Pooled Two-sample t- statistic: When two populations have the same variances. Try: # 46, 48, 53, 56

9

10

### AP Stats Chapter 13. Section 13.1: Comparing Two Means. Characteristics of two sample problems: What are the three conditions for comparing two means?

Section 13.1: Comparing Two Means Characteristics of two sample problems: AP Stats Chapter 13 What are the three conditions for comparing two means? When two population means are compared you can do one

### Unit 24 Hypothesis Tests about Means

Unit 24 Hypothesis Tests about Means Objectives: To recognize the difference between a paired t test and a two-sample t test To perform a paired t test To perform a two-sample t test A measure of the amount

### Third Midterm Exam (MATH1070 Spring 2012)

Third Midterm Exam (MATH1070 Spring 2012) Instructions: This is a one hour exam. You can use a notesheet. Calculators are allowed, but other electronics are prohibited. 1. [40pts] Multiple Choice Problems

### Test 12 Tests of Significance Homework Part 1 (Chpts & 11.2)

Name Period Test 12 Tests of Significance Homework Part 1 (Chpts. 12.2 & 11.2) 1. School officials are interested in implementing a policy that would allow students to bring their own technology to school

### Unit 27: Comparing Two Means

Unit 27: Comparing Two Means Prerequisites Students should have experience with one-sample t-procedures before they begin this unit. That material is covered in Unit 26, Small Sample Inference for One

### Statistics 2015 Scoring Guidelines

AP Statistics 2015 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home

PROBLEM SET 1 For the first three answer true or false and explain your answer. A picture is often helpful. 1. Suppose the significance level of a hypothesis test is α=0.05. If the p-value of the test

### Test of proportion = 0.5 N Sample prop 95% CI z- value p- value (0.400, 0.466)

STATISTICS FOR THE SOCIAL AND BEHAVIORAL SCIENCES Recitation #10 Answer Key PROBABILITY, HYPOTHESIS TESTING, CONFIDENCE INTERVALS Hypothesis tests 2 When a recent GSS asked, would you be willing to pay

### find confidence interval for a population mean when the population standard deviation is KNOWN Understand the new distribution the t-distribution

Section 8.3 1 Estimating a Population Mean Topics find confidence interval for a population mean when the population standard deviation is KNOWN find confidence interval for a population mean when the

### AP Statistics 2000 Scoring Guidelines

AP Statistics 000 Scoring Guidelines The materials included in these files are intended for non-commercial use by AP teachers for course and exam preparation; permission for any other use must be sought

### 1 Confidence intervals

Math 143 Inference for Means 1 Statistical inference is inferring information about the distribution of a population from information about a sample. We re generally talking about one of two things: 1.

### Unit 21 Student s t Distribution in Hypotheses Testing

Unit 21 Student s t Distribution in Hypotheses Testing Objectives: To understand the difference between the standard normal distribution and the Student's t distributions To understand the difference between

### Statistical Inference and t-tests

1 Statistical Inference and t-tests Objectives Evaluate the difference between a sample mean and a target value using a one-sample t-test. Evaluate the difference between a sample mean and a target value

### AP Statistics 2007 Scoring Guidelines

AP Statistics 2007 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college

### Testing: is my coin fair?

Testing: is my coin fair? Formally: we want to make some inference about P(head) Try it: toss coin several times (say 7 times) Assume that it is fair ( P(head)= ), and see if this assumption is compatible

### The calculations lead to the following values: d 2 = 46, n = 8, s d 2 = 4, s d = 2, SEof d = s d n s d n

EXAMPLE 1: Paired t-test and t-interval DBP Readings by Two Devices The diastolic blood pressures (DBP) of 8 patients were determined using two techniques: the standard method used by medical personnel

### AP Statistics 2001 Solutions and Scoring Guidelines

AP Statistics 2001 Solutions and Scoring Guidelines The materials included in these files are intended for non-commercial use by AP teachers for course and exam preparation; permission for any other use

### AP Statistics 2010 Scoring Guidelines

AP Statistics 2010 Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in

### LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.

### Hypothesis Testing - II

-3σ -2σ +σ +2σ +3σ Hypothesis Testing - II Lecture 9 0909.400.01 / 0909.400.02 Dr. P. s Clinic Consultant Module in Probability & Statistics in Engineering Today in P&S -3σ -2σ +σ +2σ +3σ Review: Hypothesis

### AP Statistics 2008 Scoring Guidelines Form B

AP Statistics 2008 Scoring Guidelines Form B The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students

### Unit 26: Small Sample Inference for One Mean

Unit 26: Small Sample Inference for One Mean Prerequisites Students need the background on confidence intervals and significance tests covered in Units 24 and 25. Additional Topic Coverage Additional coverage

### 1 Hypotheses test about µ if σ is not known

1 Hypotheses test about µ if σ is not known In this section we will introduce how to make decisions about a population mean, µ, when the standard deviation is not known. In order to develop a confidence

### Biostatistics: 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

### Inferences About Differences Between Means Edpsy 580

Inferences About Differences Between Means Edpsy 580 Carolyn J. Anderson Department of Educational Psychology University of Illinois at Urbana-Champaign Inferences About Differences Between Means Slide

### T adult = 96 T child = 114.

Homework Solutions Do all tests at the 5% level and quote p-values when possible. When answering each question uses sentences and include the relevant JMP output and plots (do not include the data in your

### Provide an appropriate response. Solve the problem. Determine the null and alternative hypotheses for the proposed hypothesis test.

Provide an appropriate response. 1) Suppose that x is a normally distributed variable on each of two populations. Independent samples of sizes n1 and n2, respectively, are selected from the two populations.

### Solutions 7. Review, one sample t-test, independent two-sample t-test, binomial distribution, standard errors and one-sample proportions.

Solutions 7 Review, one sample t-test, independent two-sample t-test, binomial distribution, standard errors and one-sample proportions. (1) Here we debunk a popular misconception about confidence intervals

### Sections 4.5-4.7: Two-Sample Problems. Paired t-test (Section 4.6)

Sections 4.5-4.7: Two-Sample Problems Paired t-test (Section 4.6) Examples of Paired Differences studies: Similar subjects are paired off and one of two treatments is given to each subject in the pair.

### Null Hypothesis H 0. The null hypothesis (denoted by H 0

Hypothesis test In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing a claim about a property

### Sociology 6Z03 Topic 15: Statistical Inference for Means

Sociology 6Z03 Topic 15: Statistical Inference for Means John Fox McMaster University Fall 2016 John Fox (McMaster University) Soc 6Z03: Statistical Inference for Means Fall 2016 1 / 41 Outline: Statistical

### c. The factor is the type of TV program that was watched. The treatment is the embedded commercials in the TV programs.

STAT E-150 - Statistical Methods Assignment 9 Solutions Exercises 12.8, 12.13, 12.75 For each test: Include appropriate graphs to see that the conditions are met. Use Tukey's Honestly Significant Difference

### Inferential Statistics

Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

### ACTM State Exam-Statistics

ACTM State Exam-Statistics For the 25 multiple-choice questions, make your answer choice and record it on the answer sheet provided. Once you have completed that section of the test, proceed to the tie-breaker

### CHAPTERS 4-6: Hypothesis Tests Read sections 4.3, 4.5, 5.1.5, Confidence Interval vs. Hypothesis Test (4.3):

CHAPTERS 4-6: Hypothesis Tests Read sections 4.3, 4.5, 5.1.5, 6.1.3 Confidence Interval vs. Hypothesis Test (4.3): The purpose of a confidence interval is to estimate the value of a parameter. The purpose

### 0.1 Estimating and Testing Differences in the Treatment means

0. Estimating and Testing Differences in the Treatment means Is the F-test significant, we only learn that not all population means are the same, but through this test we can not determine where the differences

### Let m denote the margin of error. Then

S:105 Statistical Methods and Computing Sample size for confidence intervals with σ known t Intervals Lecture 13 Mar. 6, 009 Kate Cowles 374 SH, 335-077 kcowles@stat.uiowa.edu 1 The margin of error The

### One-sample normal hypothesis Testing, paired t-test, two-sample normal inference, normal probability plots

1 / 27 One-sample normal hypothesis Testing, paired t-test, two-sample normal inference, normal probability plots Timothy Hanson Department of Statistics, University of South Carolina Stat 704: Data Analysis

### The Chi-Square Distributions

MATH 183 The Chi-Square Distributions Dr. Neal, WKU The chi-square distributions can be used in statistics to analyze the standard deviation " of a normally distributed measurement and to test the goodness

### An example ANOVA situation. 1-Way ANOVA. Some notation for ANOVA. Are these differences significant? Example (Treating Blisters)

An example ANOVA situation Example (Treating Blisters) 1-Way ANOVA MATH 143 Department of Mathematics and Statistics Calvin College Subjects: 25 patients with blisters Treatments: Treatment A, Treatment

BIOSTATISTICS QUIZ ANSWERS 1. When you read scientific literature, do you know whether the statistical tests that were used were appropriate and why they were used? a. Always b. Mostly c. Rarely d. Never

### The bread and butter of statistical data analysis is the Student s t-test.

03-Elliott-4987.qxd 7/18/2006 3:43 PM Page 47 3 Comparing One or Two Means Using the t-test The bread and butter of statistical data analysis is the Student s t-test. It was named after a statistician

### Chapter 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

### ABSORBENCY OF PAPER TOWELS

ABSORBENCY OF PAPER TOWELS 15. Brief Version of the Case Study 15.1 Problem Formulation 15.2 Selection of Factors 15.3 Obtaining Random Samples of Paper Towels 15.4 How will the Absorbency be measured?

### Basic Statistics. Probability and Confidence Intervals

Basic Statistics Probability and Confidence Intervals Probability and Confidence Intervals Learning Intentions Today we will understand: Interpreting the meaning of a confidence interval Calculating the

### Math 62 Statistics Sample Exam Questions

Math 62 Statistics Sample Exam Questions 1. (10) Explain the difference between the distribution of a population and the sampling distribution of a statistic, such as the mean, of a sample randomly selected

### Section 9.3B Inference for Means: Paired Data

Section 9.3B Inference for Means: Paired Data 1 Objective PERFORM significance tests for paired data are called: paired t procedures. Comparative studies (i.e. 2 observations on 1 individual or 1 observation

### The Sampling Distribution of the Mean Confidence Intervals for a Proportion

Math 130 Jeff Stratton Name The Sampling Distribution of the Mean Confidence Intervals for a Proportion Goal: To gain experience with the sampling distribution of the mean, and with confidence intervals

### AP Statistics Chapter 1 Test - Multiple Choice

AP Statistics Chapter 1 Test - Multiple Choice Name: 1. The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck. From this graph, we may conclude

### Complement: 0.4 x 0.8 = =.6

Homework Chapter 5 Name: 1. Use the graph below 1 a) Why is the total area under this curve equal to 1? Rectangle; A = LW A = 1(1) = 1 b) What percent of the observations lie above 0.8? 1 -.8 =.2; A =

### Versions 1a Page 1 of 17

Note to Students: This practice exam is intended to give you an idea of the type of questions the instructor asks and the approximate length of the exam. It does NOT indicate the exact questions or the

### 4. Introduction to Statistics

Statistics for Engineers 4-1 4. Introduction to Statistics Descriptive Statistics Types of data A variate or random variable is a quantity or attribute whose value may vary from one unit of investigation

### Example for testing one population mean:

Today: Sections 13.1 to 13.3 ANNOUNCEMENTS: We will finish hypothesis testing for the 5 situations today. See pages 586-587 (end of Chapter 13) for a summary table. Quiz for week 8 starts Wed, ends Monday

### Do the following using Mintab (1) Make a normal probability plot for each of the two curing times.

SMAM 314 Computer Assignment 4 1. An experiment was performed to determine the effect of curing time on the comprehensive strength of concrete blocks. Two independent random samples of 14 blocks were prepared

### Summary of Formulas and Concepts. Descriptive Statistics (Ch. 1-4)

Summary of Formulas and Concepts Descriptive Statistics (Ch. 1-4) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume

### AP Statistics 2013 Scoring Guidelines

AP Statistics 2013 Scoring Guidelines The College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the

### Good 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

### Final 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

### AP Statistics 2002 Scoring Guidelines

AP Statistics 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought

### Page 548, Exercise 13

Millersville University Name Answer Key Department of Mathematics MATH 130, Elements of Statistics I, Homework 4 April 29, 2008 Page 548, Exercise 13 Height versus Arm Span A statistics student believes

### LAB 4 ASSIGNMENT CONFIDENCE INTERVALS AND HYPOTHESIS TESTING. Using Data to Make Decisions

LAB 4 ASSIGNMENT CONFIDENCE INTERVALS AND HYPOTHESIS TESTING This lab assignment will give you the opportunity to explore the concept of a confidence interval and hypothesis testing in the context of a

### Death on the Titanic

Death on the Titanic Introduction On its maiden voyage, the cruise ship Titanic collided with an iceberg and sank. There was much loss of life. It is of interest to test how well sample proportions from

### Chapter 8 Hypothesis Testing

Chapter 8 Hypothesis Testing Chapter problem: Does the MicroSort method of gender selection increase the likelihood that a baby will be girl? MicroSort: a gender-selection method developed by Genetics

### 2011 # AP Exam Solutions 2011 # # # #1 5/16/2011

2011 AP Exam Solutions 1. A professional sports team evaluates potential players for a certain position based on two main characteristics, speed and strength. (a) Speed is measured by the time required

### fifty Fathoms Statistics Demonstrations for Deeper Understanding Tim Erickson

fifty Fathoms Statistics Demonstrations for Deeper Understanding Tim Erickson Contents What Are These Demos About? How to Use These Demos If This Is Your First Time Using Fathom Tutorial: An Extended Example

### Difference of Means and ANOVA Problems

Difference of Means and Problems Dr. Tom Ilvento FREC 408 Accounting Firm Study An accounting firm specializes in auditing the financial records of large firm It is interested in evaluating its fee structure,particularly

### MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW. Ch 1-3. One problem similar to the problems below will be included in the final

MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW Ch 1-3 One problem similar to the problems below will be included in the final 1.This table presents the price distribution of shoe styles offered

### AP * Statistics Review

AP * Statistics Review Confidence Intervals Teacher Packet AP* is a trademark of the College Entrance Examination Board. The College Entrance Examination Board was not involved in the production of this

### Hypothesis Tests Means 2 samples

Hypothesis Tests Means 2 samples 1. More eggs? Can a food additive increase egg production? Agricultural researchers want to design an experiment to find out. They have 100 hens available. They have two

### AP Statistics Semester Exam Review Chapters 1-3

AP Statistics Semester Exam Review Chapters 1-3 1. Here are the IQ test scores of 10 randomly chosen fifth-grade students: 145 139 126 122 125 130 96 110 118 118 To make a stemplot of these scores, you

### AP Statistics 2006 Scoring Guidelines

AP Statistics 2006 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college

### Comparing Means in Two Populations

Comparing Means in Two Populations Overview The previous section discussed hypothesis testing when sampling from a single population (either a single mean or two means from the same population). Now we

### CHAPTER 14 NONPARAMETRIC TESTS

CHAPTER 14 NONPARAMETRIC TESTS Everything that we have done up until now in statistics has relied heavily on one major fact: that our data is normally distributed. We have been able to make inferences

### AP Statistics Hypothesis Testing Chapter 9. Intro to Significance Tests

Intro to Significance Tests Name Hr For the following pairs, indicate whether they are legitimate hypotheses and why. 1. 2. 3. 4. For each situation, state the null and alternate hypothesis. (Define your

### AP Statistics 2012 Scoring Guidelines

AP Statistics 2012 Scoring Guidelines The College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the

### Multiple Choice Questions

Multiple Choice Questions 1. A fast- food restaurant chain with 700 outlets in the United States describes the geographic location of its restaurants with the accompanying table of percentages. A restaurant

### AP Statistics 2005 Scoring Guidelines

AP Statistics 2005 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college

### - Inter-Quartile Range, - Outliers, - Boxplots.

Today: - Inter-Quartile Range, - Outliers, - Boxplots. Reading for today: Start Chapter 4. Quartiles and the Five Number Summary - The five numbers are the Minimum (Q0), Lower Quartile (Q1), Median (Q2),

### The 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

### Statistics 2014 Scoring Guidelines

AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home

### 6. Duality between confidence intervals and statistical tests

6. Duality between confidence intervals and statistical tests Suppose we carry out the following test at a significance level of 100α%. H 0 :µ = µ 0 H A :µ µ 0 Then we reject H 0 if and only if µ 0 does

### Statistiek I. t-tests. John Nerbonne. CLCG, Rijksuniversiteit Groningen. John Nerbonne 1/35

Statistiek I t-tests John Nerbonne CLCG, Rijksuniversiteit Groningen http://wwwletrugnl/nerbonne/teach/statistiek-i/ John Nerbonne 1/35 t-tests To test an average or pair of averages when σ is known, we

### MTH 140 Statistics Videos

MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative

### 12.1 Inference for Linear Regression

12.1 Inference for Linear Regression Least Squares Regression Line y = a + bx You might want to refresh your memory of LSR lines by reviewing Chapter 3! 1 Sample Distribution of b p740 Shape Center Spread

### Statistics for Management II-STAT 362-Final Review

Statistics for Management II-STAT 362-Final Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. The ability of an interval estimate to

### Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS

Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS Choose the single best answer for each question. Discuss questions with classmates, TAs and Professor Whitten. Raise your hand to check

### General Method: Difference of Means. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n 1, n 2 ) 1.

General Method: Difference of Means 1. Calculate x 1, x 2, SE 1, SE 2. 2. Combined SE = SE1 2 + SE2 2. ASSUMES INDEPENDENT SAMPLES. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n

### Name: Date: Use the following to answer questions 3-4:

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

### Estimating and Finding Confidence Intervals

. Activity 7 Estimating and Finding Confidence Intervals Topic 33 (40) Estimating A Normal Population Mean μ (σ Known) A random sample of size 10 from a population of heights that has a normal distribution

### Instructor: Doug Ensley Course: MAT Applied Statistics - Ensley

Student: Date: Instructor: Doug Ensley Course: MAT117 01 Applied Statistics - Ensley Assignment: Online 15 - Sections 8.2-8.3 1. A survey asked the question "What do you think is the ideal number of children

### 12 Hypothesis Testing

CHAPTER 12 Hypothesis Testing Chapter Outline 12.1 HYPOTHESIS TESTING 12.2 CRITICAL VALUES 12.3 ONE-SAMPLE T TEST 247 12.1. Hypothesis Testing www.ck12.org 12.1 Hypothesis Testing Learning Objectives Develop

### Unit 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

### 10-3 Measures of Central Tendency and Variation

10-3 Measures of Central Tendency and Variation So far, we have discussed some graphical methods of data description. Now, we will investigate how statements of central tendency and variation can be used.

### Data Mining Part 2. Data Understanding and Preparation 2.1 Data Understanding Spring 2010

Data Mining Part 2. and Preparation 2.1 Spring 2010 Instructor: Dr. Masoud Yaghini Introduction Outline Introduction Measuring the Central Tendency Measuring the Dispersion of Data Graphic Displays References

### Recall this chart that showed how most of our course would be organized:

Chapter 4 One-Way ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical

### When σ Is Known: Recall the Mystery Mean Activity where x bar = 240.79 and we have an SRS of size 16

8.3 ESTIMATING A POPULATION MEAN When σ Is Known: Recall the Mystery Mean Activity where x bar = 240.79 and we have an SRS of size 16 Task was to estimate the mean when we know that the situation is Normal

### Section I: Multiple Choice Select the best answer for each question.

Chapter 15 (Regression Inference) AP Statistics Practice Test (TPS- 4 p796) Section I: Multiple Choice Select the best answer for each question. 1. Which of the following is not one of the conditions that

### Chapter 16 Multiple Choice Questions (The answers are provided after the last question.)

Chapter 16 Multiple Choice Questions (The answers are provided after the last question.) 1. Which of the following symbols represents a population parameter? a. SD b. σ c. r d. 0 2. If you drew all possible