2009 the humongous book of statistics

Chapter 9: Confidence Intervals 219Introduction to Confidence Intervals for the Mean ...220 Confidence Intervals for the Mean with Large Samples and Sigma Known ...221 Confidence Intervals f

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Copyright © 2009 by W Michael Kelley

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IN 46240

Library of Congress Catalog Card Number: 2006926601

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ISBN: 1-101-15010-6

Introduction

Frequency Distributions 2

Histograms 5

Bar Charts 8

Pie Charts 14

Line Charts 19

Scatter Charts 21

Chapter 2: Calculating Descriptive Statistics: Measures of Central Tendency 25 Mean 26

Median 30

Midrange 32

Mode 33

Percentile 36

Weighted Mean 42

Mean of a Frequency Distribution 45

Mean of a Grouped Frequency Distribution 47

Chapter 3: Calculating Descriptive Statistics: Measures of Variation 51 Range 52

Interquartile Range 54

Outliers 58

Visualizing Distributions 62

Stem-and-Leaf Plot 66

Variance and Standard Deviation of a Population 71

Variance and Standard Deviation for Grouped Data 81

Chebyshev’s Theorem 85

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Chapter 4: Introduction to Probability 89

Types of Probability 90

Ađition Rules for Probability 98

Conditional Probability 106

The Multiplication Rule for Probability .116

Bayes’ Theorem 120

Chapter 5: Counting Principles and Probability Distributions 123 Fundamental Counting Principle 124

Permutations 127

Combinations 129

Probability Distributions .135

Chapter 6: Discrete Probability Distributions 141 Binomial Probability Distribution 142

Poisson Probability Distribution .149

The Poisson Distribution as an Approximation to the Binomial Distribution .156

Hypergeometric Probability Distribution 159

Chapter 7: Continuous Probability Distributions 165 Normal Pobability Distribution .166

The Empirical Rule .179

Using the Normal Distribution to Approximate the Binomial Distribution .182

Continuous Uniform Distribution .186

Exponential Distribution 189

Chapter 8: Sampling and Sampling Distributions 195 Probability Sampling .196

Sampling Distribution of the Mean 197

Finite Population Correction Factor .205

Sampling Distribution of the Proportion .207

Finite Population Correction Factor for the Sampling Distribution of the Proportion 215

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Chapter 9: Confidence Intervals 219

Introduction to Confidence Intervals for the Mean .220

Confidence Intervals for the Mean with Large Samples and Sigma Known 221

Confidence Intervals for the Mean with Small Samples and Sigma Known 225

Confidence Intervals for the Mean with Small Samples and Sigma Unknown .229

Confidence Intervals for the Mean with Large Samples and Sigma Unknown .235

Confidence Intervals for the Proportion .239

Chapter 10: Hypothesis Testing for a Single Population 243 Introduction to Hypothesis Testing for the Mean .244

Hypothesis Testing for the Mean with n v 30 and Sigma Known .247

Hypothesis Testing for the Mean with n < 30 and Sigma Known .255

Hypothesis Testing for the Mean with n < 30 and Sigma Unknown .259

Hypothesis Testing for the Mean with n > 30 and Sigma Unknown .265

Hypothesis Testing for the Proportion .271

Chapter 11: Hypothesis Testing for Two Populations 279 Hypothesis Testing for Two Means with n > 30 and Sigma Known .280

Hypothesis Testing for Two Means with n < 30 and Sigma Known .286

Hypothesis Testing for Two Means with n < 30 and Sigma Unknown .289

Hypothesis Testing for Two Means with n v 30 and Sigma Unknown .299

Hypothesis Testing for Two Means with Dependent Samples .302

Hypothesis Testing for Two Proportions .309

Chapter 12: Chi-Square and Variance Tests 317 Chi-Square Goodness-of-Fit Test 318

Chi-Square Test for Independence .331

Hypothesis Test for a Single Population Variance .338

Hypothesis Test for Two Population Variances .346

Chapter 13: Analysis of Variance 351 One-Way ANOVA: Completely Randomized Design .352

One-Way ANOVA: Randomized Block Design .371

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Chapter 14: Correlation and Simple Regression Analysis 389

Correlation 390

Simple Regression Analysis .396

Chapter 15: Nonparametric Tests 413 The Sign Test with a Small Sample Size 414

The Sign Test with a Large Sample Size 418

The Paired-Sample Sign Test (n f 25) 421

The Paired-Sample Sign Test (n # 25) 423

The Wilcoxon Rank Sum Test for Small Samples .425

The Wilcoxon Rank Sum Test for Large Samples .428

The Wilcoxon Signed-Rank Test .431

The Kruskal-Wallis Test 436

The Spearman Rank Correlation Coefficient Test .442

Chapter 16: Forecasting 449 Simple Moving Average .450

Weighted Moving Average .454

Exponential Smoothing 458

Exponential Smoothing with Trend Adjustment 462

Trend Projection and Seasonality .468

Causal Forecasting 477

Chapter 17: Statistical Process Control 483 Introduction to Statistical Process Control 484

Statistical Process Control for Variable Measurement .484

Statistical Process Control for Attribute Measurement Using p-charts 491

Statistical Process Control for Attribute Measurement Using c-charts 495

Process Capability Ratio 498

Process Capability Index .500

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Chapter 18: Contextualizing Statistical Concepts 503

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Chapter 1

DISPLAYING DESCRIPTIVE STATISTICS

The main focus of descriptive statistics is to summarize and present data This chapter demonstrates a variety of techniques available to display descriptive statistics Presenting data graphically allows the user to extract information more efficiently.

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1.1 Develop a frequency distribution summarizing this data.

A frequency distribution is a two-column table In the left column, list each value in the data set from least to greatest Count the number of times each value appears and record those totals in the right column

Note: Problems 1.1–1.3 refer to the data set in Problem 1.1, the daily demand for hammers at

a hardware store over the last 20 days.

1.2 Develop a relative frequency distribution for the data

Divide the frequency of each daily demand by the total number of data values (20)

Daily Demand Frequency Relative Frequency

Note: Problems 1.1–1.3 refer to the data set in Problem 1.1, the daily demand for hammers at

a hardware store over the last 20 days.

1.3 Develop a cumulative relative frequency distribution for the data

Note: Problems 1.4–1.6 refer to the data set below, the number of calls per day made from a

cell phone for the past 30 days.

Cell Phone Calls per Day

1.4 Develop a frequency distribution summarizing the data

Because this data has many possible outcomes, you should group the number

of calls per day into groups, which are known as classes One option is the 2 k v n

rule to determine the number of classes, where k equals the number of classes

and n equals the number of data points Given n = 30, the best value for k is 5.

Calculate the width W of each class.

Set the size of each class to 3 and list the classes in the left column of the

frequency distribution Count the number of values contained in each group

and list those values in the right column

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Calls per Day Frequency

1.5 Develop a relative frequency distribution for the data

Divide the frequency of each class by the total number of data values (30)

Calls per Day Frequency Relative Frequency

1.6 Develop a cumulative relative frequency distribution for the data

The cumulative relative frequency for a particular row is the relative frequency (calculated in Problem 1.5) for that row plus the cumulative relative frequency for the previous row

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1.8 Develop a histogram for the frequency distribution below, the commuting distance for 50 employees of a particular company.

First, develop a frequency distribution for the data Using the 2k v n rule, set

k = 6 because 26= 64 v 40 Calculate the width W of each class.

Set the size of each class equal to 10 and count the number of values contained

Miles per Tank Frequency

The height of each bar in the histogram reflects the frequency for each group

of miles per tank of gas

1.10 Develop a histogram for the data set below, the number of home runs hit by 40

Major League Baseball players during the 2008 season

Develop a frequency distribution for the data Apply the 2k v n rule and set k = 6

because 26= 64 v 40 Calculate the width W of each class.

Set the size of each class equal to 4 and count the number of values contained

Home Runs Frequency

A column bar chart uses vertical bars to represent categorical data The height

of each bar corresponds to the value of each category

1.12 Construct a column bar chart for the data below, a company’s monthly sales

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1.13 Construct a horizontal bar chart for the data set below, weekly donations collected at a local church.

Note: Problems 1.15–1.16 refer to the data set below, weekly sales data in units for

1.15 Construct a grouped column bar chart for the data, grouping by week

Because there are two data values for each time period (a value for Store 1 and

a value for Store 2), you should use a grouped column bar chart

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Note: Problems 1.15–1.16 refer to the data set in Problem 1.15, weekly sales data in units for two stores.

1.16 Construct a stacked column bar chart for the data, grouping by store

Each column represents the total units sold each week between the two stores

Note: Problems 1.17–1.20 refer to the data set below, the investment portfolio for three different investors in thousands of dollars.

Investor 1 Investor 2 Investor 3

1.17 Construct a grouped horizontal bar chart, grouping by investor

Three horizontal bars are arranged side-by-side for each investor, indicating the amount of each investment type

Note: Problems 1.17–1.20 refer to the data set in Problem 1.17, showing the investment

portfolio for three different investors in thousands of dollars.

1.18 Construct a grouped horizontal bar chart, grouping by investment type

Arrange three horizontal bars representing the investors, side-by-side, for each

investment type

Note: Problems 1.17–1.20 refer to the data set in Problem 1.17, the investment portfolio for

three different investors in thousands of dollars.

1.19 Construct a stacked horizontal bar chart, grouping by investor

Each investor is represented by three horizontally stacked bars that indicate that

investor’s total investments by type

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Note: Problems 1.17–1.20 refer to the data set in Problem 1.17, the investment portfolio for three different investors in thousands of dollars.

1.20 Construct a stacked horizontal bar chart, grouping by investment type.Represent each investment type using three horizontally stacked bars

Multiply each relative frequency distribution by 360 to calculate the

corresponding central angle for each category in the pie chart A central

angle has a vertex at the center of the circle and sides that intersect the circle,

defining the boundaries of each category in a pie chart

Grade Relative Frequency Central Angle

The central angle determines the size of each pie segment

1.22 Construct a pie chart for the data in the table below, the number of total wins

recorded by the Green Bay Packers football team in five recent seasons

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1.23 Construct a pie chart for the data in the table below, an individual investor’s

The total investment is $78,000 Divide the figure for each category by this

number to determine the percentage of the total investment each category

Multiply each percentage by 360 to calculate the central angle for each category

in the pie chart

Use the central angles calculated above to draw appropriately sized sectors of

the pie chart If you have difficulty visualizing angles, use a protractor

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1.24 Construct a pie chart for the frequency distribution below, the daily high temperature (in degrees Fahrenheit) in a particular city over the last 40 days.

Determine the relative frequency distribution for each temperature range

Daily High Temperature Frequency Relative Frequency

Calculate the central angle for each category in the pie chart

Line Charts

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1.25 Construct a line chart for the data in the table below, the number of wins

recorded by the Philadelphia Phillies for seven seasons

Place the time variable (year) on the x-axis and place the variable of interest

(wins) on the y-axis.

1.26 Construct a line chart for the data in the table below, the percent change in

annual profit for a company by year

Place the time variable (year) on the x-axis and place the variable of interest (percent change) on the y-axis.

1.27 Construct a line chart for the data in the table below, the population of Delaware by decade during the 1800s

Scatter Charts

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1.28 Construct a scatter chart for the data in the table below, the number of hours

eight students studied for an exam and the scores they earned on the exam

Place the independent variable (study hours) on the x-axis and the dependent

variable (exam score) on the y-axis.

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1.29 Construct a scatter chart for the data below, the mileage and selling price of eight used cars.

1.30 Construct a scatter chart for the data in the table below, eight graduate

students’ grade point averages (GPA) and entrance exam scores for M.B.A

Place the independent variable (GMAT) on the x-axis and the dependent

variable (GPA) on the y-axis.



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Chapter 2

CALCULATING DESCRIPTIVE STATISTICS: MEASURES OF CENTRAL TENDENCY

One of the most common roles served by descriptive statistics is termining the central tendency of data This chapter investigates the primary means by which the “center” of a data set can be described, including the mean, median, mode, and percentiles.

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2.1 The table below lists the number of students enrolled in the five different statistics courses offered by a college Calculate the mean number of students per class

Number of Students

The mean µ of a data set is the sum of the data divided by the population size.

Notice that a mean can be heavily influenced by an extreme value in the data The only difference between the enrollment numbers in Problems 2.1 and 2.2

is the size of the last class That class increased from 15 to 75 students and caused the mean class size to grow from 21.2 to 33.2

2.3 The table below lists the time, in minutes, it takes seven random customers to check out at a local grocery store Calculate the mean time it takes a customer

2.4 A consumer group tested the gas mileage of two car models in five trials

Which model averages more miles per gallon?

Trial 1 Trial 2 Trial 3 Trial 4 Trial 5

Model B averages more miles per gallon than Model A

2.5 The table below reports the number of minutes eight randomly selected airline

flights were either early (negative values) or late (positive values) arriving at

their destinations Calculate the sample mean

Number of Minutes Early or Late

Combine the positive and negative values and divide by the sample size

The average flight is 8.6 minutes late

2.6 The following table lists the daily percent increase (or decrease) of a stock

price over a five-day period Calculate the mean daily change in the stock price

Percent Increase or Decrease

If the sum is less than zero, the average change is a decrease, whereas a

positive sum indicates an average increase

The stock price decreased an average of 1.76 percent per day

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2.7 The table below lists the points scored by three basketball players over six games Identify the player with the highest average points per game.

Player Points Scored per Game

Calculate each player’s scoring average separately

Paul averaged the most points per game, 21.7

Note: Problems 2.8–2.9 refer to the data set below, the daily demand for tires at a particular store over a seven-day period.

The demand forecast for January 11 is 29.3 tires