9.2 Examples. Example 1

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "9.2 Examples. Example 1"

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)

Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS

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

More information

Point and Interval Estimates

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 information

Confidence Intervals

Confidence 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 information

Statistical Inference

Statistical Inference Statistical Inference Idea: Estimate parameters of the population distribution using data. How: Use the sampling distribution of sample statistics and methods based on what would happen if we used this

More information

Lesson 17: Margin of Error When Estimating a Population Proportion

Lesson 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 information

Confidence Intervals for Coefficient Alpha

Confidence Intervals for Coefficient Alpha Chapter 818 Confidence Intervals for Coefficient Alpha Introduction Coefficient alpha, or Cronbach s alpha, is a measure of the reliability of a test consisting of k parts. The k parts usually represent

More information

Math 251, Review Questions for Test 3 Rough Answers

Math 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 information

SAMPLING DISTRIBUTIONS

SAMPLING 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 information

Chapter 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. 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 information

Use Measures of Central Tendency and Dispersion. Measures of Central Tendency

Use Measures of Central Tendency and Dispersion. Measures of Central Tendency 13.6 Use Measures of Central Tendency and Dispersion Before You analyzed surveys and samples. Now You will compare measures of central tendency and dispersion. Why? So you can analyze and compare data,

More information

Prob & Stats. Chapter 9 Review

Prob & Stats. Chapter 9 Review Chapter 9 Review Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally

More information

CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING

CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING MULTIPLE CHOICE 56. In testing the hypotheses H 0 : µ = 50 vs. H 1 : µ 50, the following information is known: n = 64, = 53.5, and σ = 10. The standardized

More information

Sampling Distribution of a Sample Proportion

Sampling 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 information

Week 4: Standard Error and Confidence Intervals

Week 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 information

Probability Distributions

Probability 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 information

4. Introduction to Statistics

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

More information

c. Construct a boxplot for the data. Write a one sentence interpretation of your graph.

c. 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 information

Confidence Intervals for Cpk

Confidence 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 information

p ˆ (sample mean and sample

p 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 information

Confidence Intervals for One Standard Deviation Using Standard Deviation

Confidence 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 information

An interval estimate (confidence interval) is an interval, or range of values, used to estimate a population parameter. For example 0.476<p<0.

An interval estimate (confidence interval) is an interval, or range of values, used to estimate a population parameter. For example 0.476<p<0. Lecture #7 Chapter 7: Estimates and sample sizes In this chapter, we will learn an important technique of statistical inference to use sample statistics to estimate the value of an unknown population parameter.

More information

Margin of Error When Estimating a Population Proportion

Margin of Error When Estimating a Population Proportion Margin of Error When Estimating a Population Proportion Student Outcomes Students use data from a random sample to estimate a population proportion. Students calculate and interpret margin of error in

More information

AP * Statistics Review

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

More information

MEASURES OF VARIATION

MEASURES 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 information

Homework 5 Solutions

Homework 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 information

Confidence Intervals for Cp

Confidence 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 information

Chapter Study Guide. Chapter 11 Confidence Intervals and Hypothesis Testing for Means

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

More information

Confidence level. Most common choices are 90%, 95%, or 99%. (α = 10%), (α = 5%), (α = 1%)

Confidence level. Most common choices are 90%, 95%, or 99%. (α = 10%), (α = 5%), (α = 1%) Confidence Interval A confidence interval (or interval estimate) is a range (or an interval) of values used to estimate the true value of a population parameter. A confidence interval is sometimes abbreviated

More information

STATISTICS 8 CHAPTERS 1 TO 6, SAMPLE MULTIPLE CHOICE QUESTIONS

STATISTICS 8 CHAPTERS 1 TO 6, SAMPLE MULTIPLE CHOICE QUESTIONS STATISTICS 8 CHAPTERS 1 TO 6, SAMPLE MULTIPLE CHOICE QUESTIONS Correct answers are in bold italics.. This scenario applies to Questions 1 and 2: A study was done to compare the lung capacity of coal miners

More information

Section 5 3 The Mean and Standard Deviation of a Binomial Distribution

Section 5 3 The Mean and Standard Deviation of a Binomial Distribution Section 5 3 The Mean and Standard Deviation of a Binomial Distribution Previous sections required that you to find the Mean and Standard Deviation of a Binomial Distribution by using the values from a

More information

4. Continuous Random Variables, the Pareto and Normal Distributions

4. 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 information

DOT HS 811 377 September 2010. The 2009 National Survey of the Use of Booster Seats

DOT HS 811 377 September 2010. The 2009 National Survey of the Use of Booster Seats DOT HS 811 377 September 2010 The 2009 National Survey of the Use of Booster Seats Disclaimer This publication is distributed by the U.S. Department of Transportation, National Highway Traffic Safety Administration,

More information

Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:

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

More information

MATH 103/GRACEY PRACTICE EXAM/CHAPTERS 2-3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MATH 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 information

Mind on Statistics. Chapter 10

Mind 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 information

Hypothesis Testing. Bluman Chapter 8

Hypothesis Testing. Bluman Chapter 8 CHAPTER 8 Learning Objectives C H A P T E R E I G H T Hypothesis Testing 1 Outline 8-1 Steps in Traditional Method 8-2 z Test for a Mean 8-3 t Test for a Mean 8-4 z Test for a Proportion 8-5 2 Test for

More information

Data Analysis Tools. Tools for Summarizing Data

Data 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 information

Standard Deviation Calculator

Standard Deviation Calculator CSS.com Chapter 35 Standard Deviation Calculator Introduction The is a tool to calculate the standard deviation from the data, the standard error, the range, percentiles, the COV, confidence limits, or

More information

Basic Statistics. Probability and Confidence Intervals

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

More information

Probability and Statistics Lecture 9: 1 and 2-Sample Estimation

Probability and Statistics Lecture 9: 1 and 2-Sample Estimation Probability and Statistics Lecture 9: 1 and -Sample Estimation to accompany Probability and Statistics for Engineers and Scientists Fatih Cavdur Introduction A statistic θ is said to be an unbiased estimator

More information

Density 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: 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 information

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

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

More information

Note you select the cumulative probability to get the probability from 0 to 200. Cumulative Distribution Function. Binomial with n = 704 and p = 0.

Note you select the cumulative probability to get the probability from 0 to 200. Cumulative Distribution Function. Binomial with n = 704 and p = 0. GSB420 LAB3 Instructions and Assignment: Probability Distribution and Hypothesis Tests using Minitab 1. Binomial Distribution Example Ichiro Suzuki s hit. In 2004, Ichiro Suzuki of the Seattle Mariners

More information

Calculation 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 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 information

Treatment and analysis of data Applied statistics Lecture 3: Sampling and descriptive statistics

Treatment and analysis of data Applied statistics Lecture 3: Sampling and descriptive statistics Treatment and analysis of data Applied statistics Lecture 3: Sampling and descriptive statistics Topics covered: Parameters and statistics Sample mean and sample standard deviation Order statistics and

More information

Chapter 5 Analysis of variance SPSS Analysis of variance

Chapter 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 information

Chapter 3: Data Description Numerical Methods

Chapter 3: Data Description Numerical Methods Chapter 3: Data Description Numerical Methods Learning Objectives Upon successful completion of Chapter 3, you will be able to: Summarize data using measures of central tendency, such as the mean, median,

More information

Week 3&4: Z tables and the Sampling Distribution of X

Week 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 information

HypoTesting. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

HypoTesting. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Name: Class: Date: HypoTesting Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A Type II error is committed if we make: a. a correct decision when the

More information

Unit 26 Estimation with Confidence Intervals

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

More information

Sample Exam #1 Elementary Statistics

Sample Exam #1 Elementary Statistics Sample Exam #1 Elementary Statistics Instructions. No books, notes, or calculators are allowed. 1. Some variables that were recorded while studying diets of sharks are given below. Which of the variables

More information

5.1 Identifying the Target Parameter

5.1 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 information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. STATISTICS/GRACEY EXAM 3 PRACTICE/CH. 8-9 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the P-value for the indicated hypothesis test. 1) A

More information

Objective To introduce the concept of square roots and the use of the square-root key on a calculator. Assessment Management

Objective 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 information

Characteristics of Binomial Distributions

Characteristics 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 information

Confidence Intervals for the Difference Between Two Means

Confidence 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 information

Construct a scatterplot for the given data. 2) x Answer:

Construct a scatterplot for the given data. 2) x Answer: Review for Test 5 STA 2023 spr 2014 Name Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents

More information

Chapter 19 Confidence Intervals for Proportions

Chapter 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 information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Stats: Test Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Provide an appropriate response. ) Given H0: p 0% and Ha: p < 0%, determine

More information

Power and Sample Size Determination

Power and Sample Size Determination Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 Power 1 / 31 Experimental Design To this point in the semester,

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data. 1) Bill kept track of the number of hours he spent

More information

Factorial Analysis of Variance

Factorial Analysis of Variance Chapter 560 Factorial Analysis of Variance Introduction A common task in research is to compare the average response across levels of one or more factor variables. Examples of factor variables are income

More information

Practice problems for Homework 12 - confidence intervals and hypothesis testing. Open the Homework Assignment 12 and solve the problems.

Practice 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 information

You flip a fair coin four times, what is the probability that you obtain three heads.

You 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 information

Stats Review Chapters 9-10

Stats 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 information

Cents and the Central Limit Theorem Overview of Lesson GAISE Components Common Core State Standards for Mathematical Practice

Cents and the Central Limit Theorem Overview of Lesson GAISE Components Common Core State Standards for Mathematical Practice Cents and the Central Limit Theorem Overview of Lesson In this lesson, students conduct a hands-on demonstration of the Central Limit Theorem. They construct a distribution of a population and then construct

More information

What is Statistic? OPRE 6301

What 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 information

Means, standard deviations and. and standard errors

Means, 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 information

Standard Deviation Estimator

Standard 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 information

p1^ = 0.18 p2^ = 0.12 A) 0.150 B) 0.387 C) 0.300 D) 0.188 3) n 1 = 570 n 2 = 1992 x 1 = 143 x 2 = 550 A) 0.270 B) 0.541 C) 0.520 D) 0.

p1^ = 0.18 p2^ = 0.12 A) 0.150 B) 0.387 C) 0.300 D) 0.188 3) n 1 = 570 n 2 = 1992 x 1 = 143 x 2 = 550 A) 0.270 B) 0.541 C) 0.520 D) 0. Practice for chapter 9 and 10 Disclaimer: the actual exam does not mirror this. This is meant for practicing questions only. The actual exam in not multiple choice. Find the number of successes x suggested

More information

Calculate Confidence Intervals Using the TI Graphing Calculator

Calculate Confidence Intervals Using the TI Graphing Calculator Calculate Confidence Intervals Using the TI Graphing Calculator Confidence Interval for Population Proportion p Confidence Interval for Population μ (σ is known 1 Select: STAT / TESTS / 1-PropZInt x: number

More information

Statistics 151 Practice Midterm 1 Mike Kowalski

Statistics 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 information

Discrete Random Variables and their Probability Distributions

Discrete Random Variables and their Probability Distributions CHAPTER 5 Discrete Random Variables and their Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Discrete Random Variable

More information

DOT HS 812 037 June 2014. The 2013 National Survey of the Use of Booster Seats

DOT HS 812 037 June 2014. The 2013 National Survey of the Use of Booster Seats DOT HS 812 037 June 2014 The 2013 National Survey of the Use of Booster Seats DISCLAIMER This publication is distributed by the U.S. Department of Transportation, National Highway Traffic Safety Administration,

More information

Hypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam

Hypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam Hypothesis Testing 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Hypothesis Testing... 3 3. Hypothesis Tests Concerning the Mean... 10 4. Hypothesis Tests

More information

Estimation of the Mean and Proportion

Estimation of the Mean and Proportion 1 Excel Manual Estimation of the Mean and Proportion Chapter 8 While the spreadsheet setups described in this guide may seem to be getting more complicated, once they are created (and tested!), they will

More information

Continuing, we get (note that unlike the text suggestion, I end the final interval with 95, not 85.

Continuing, 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 information

FINAL EXAM REVIEW - Fa 13

FINAL EXAM REVIEW - Fa 13 FINAL EXAM REVIEW - Fa 13 Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. 1) The temperatures of eight different plastic spheres. 2) The sample

More information

AP Statistics 2013 Free-Response Questions

AP Statistics 2013 Free-Response Questions AP Statistics 2013 Free-Response Questions About the College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in

More information

Math 201: Statistics November 30, 2006

Math 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 information

To switch back to the ordinary annuity mode, enter

To switch back to the ordinary annuity mode, enter HANDBOOK: HOW TO USE YOUR HP 12C CALCULATOR This document is designed to provide you with (1) the basics of how your HP 12C financial calculator operates, and (2) the typical keystrokes that will be required

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Review Test 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use common sense to determine whether the given event is impossible; possible, but very

More information

Inferential Statistics

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

More information

Statistical Inference and t-tests

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

More information

Def: The standard normal distribution is a normal probability distribution that has a mean of 0 and a standard deviation of 1.

Def: 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 information

Chapter 2 - Graphical Summaries of Data

Chapter 2 - Graphical Summaries of Data Chapter 2 - Graphical Summaries of Data Data recorded in the sequence in which they are collected and before they are processed or ranked are called raw data. Raw data is often difficult to make sense

More information

Sampling Distribution of a Normal Variable

Sampling Distribution of a Normal Variable Ismor Fischer, 5/9/01 5.-1 5. Formal Statement and Examples Comments: Sampling Distribution of a Normal Variable Given a random variable. Suppose that the population distribution of is known to be normal,

More information

Lesson 2: Calculating Probabilities of Events Using Two-Way Tables

Lesson 2: Calculating Probabilities of Events Using Two-Way Tables Calculating Probabilities of Events Using Two-Way Tables Classwork Example 1: Building a New High School The school board of Waldo, a rural town in the Midwest, is considering building a new high school

More information

AP Statistics Hypothesis Testing Chapter 9. Intro to Significance Tests

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

More information

5/31/2013. 6.1 Normal Distributions. Normal Distributions. Chapter 6. Distribution. The Normal Distribution. Outline. Objectives.

5/31/2013. 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 information

Constructing and Interpreting Confidence Intervals

Constructing 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 information

7.6 Approximation Errors and Simpson's Rule

7.6 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 information

An Introduction to Sampling

An Introduction to Sampling An Introduction to Sampling Sampling is the process of selecting a subset of units from the population. We use sampling formulas to determine how many to select because it is based on the characteristics

More information

Calculate and interpret confidence intervals for one population average and one population proportion.

Calculate and interpret confidence intervals for one population average and one population proportion. 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 information

GrowingKnowing.com 2011

GrowingKnowing.com 2011 GrowingKnowing.com 2011 GrowingKnowing.com 2011 1 Estimates We are often asked to predict the future! When will you complete your team project? When will you make your first million dollars? When will

More information

Copyright 2013 by Laura Schultz. All rights reserved. Page 1 of 6

Copyright 2013 by Laura Schultz. All rights reserved. Page 1 of 6 Using Your TI-NSpire Calculator: Binomial Probability Distributions Dr. Laura Schultz Statistics I This handout describes how to use the binompdf and binomcdf commands to work with binomial probability

More information

! x sum of the entries

! x sum of the entries 3.1 Measures of Central Tendency (Page 1 of 16) 3.1 Measures of Central Tendency Mean, Median and Mode! x sum of the entries a. mean, x = = n number of entries Example 1 Find the mean of 26, 18, 12, 31,

More information

Chapter 8. Hypothesis Testing

Chapter 8. Hypothesis Testing Chapter 8 Hypothesis Testing Hypothesis 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

More information

The Big 50 Revision Guidelines for S1

The Big 50 Revision Guidelines for S1 The Big 50 Revision Guidelines for S1 If you can understand all of these you ll do very well 1. Know what is meant by a statistical model and the Modelling cycle of continuous refinement 2. Understand

More information

Gambling participation: activities and mode of access

Gambling 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 information