Solution Manual for Essential Statistics, 3rd Edition

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SOLUTIONS MANUAL
P AMELA O MER
Western New England University
E SSENTIAL S TATISTICS : E XPLORING
THE W ORLD T HROUGH D ATA
THIRD EDITION
Robert Gould
University of California, Los Angeles
Rebecca Wong
West Valley College
Colleen Ryan
Moorpark Community College

iii
CONTENTS
Chapter 1: Introduction to Data
Section 1.2: Classifying and Storing Data .....................................................................1
Section 1.3: Investigating Data ......................................................................................3
Section 1.4: Organizing Categorical Data .....................................................................3
Section 1.5: Collecting Data to Understand Causality...................................................6
Chapter Review Exercises .............................................................................................7
Chapter 2: Picturing Variation with Graphs
Section 2.1: Visualizing Variation in Numerical Data
and Section 2.2: Summarizing Important Features of a Numerical Distribution ....9
Section 2.3: Visualizing Variation in Categorical Variables
and Section 2.4: Summarizing Categorical Distributions ......................................14
Section 2.5: Interpreting Graphs ..................................................................................15
Chapter Review Exercises ...........................................................................................16
Chapter 3: Numerical Summaries of Center and Variation
Section 3.1: Summaries for Symmetric Distributions .................................................19
Section 3.2: What’s Unusual? The Empirical Rule and z-Scores ................................22
Section 3.3: Summaries for Skewed Distributions ......................................................23
Section 3.4: Comparing Measures of Center ...............................................................24
Section 3.5: Using Boxplots for Displaying Summaries .............................................27
Chapter Review Exercises ...........................................................................................28
Chapter 4: Regression Analysis: Exploring Associations
between Variables
Section 4.1: Visualizing Variability with a Scatterplot ...............................................31
Section 4.2: Measuring Strength of Association with Correlation ..............................31
Section 4.3: Modeling Linear Trends ..........................................................................32
Section 4.4: Evaluating the Linear Model ...................................................................37
Chapter Review Exercises ...........................................................................................40
Chapter 5: Modeling Variation with Probability
Section 5.1: What Is Randomness? ..............................................................................49
Section 5.2: Finding Theoretical Probabilities.............................................................49
Section 5.3: Associations in Categorical Variables .....................................................54
Section 5.4: Finding Empirical and Simulated Probabilities .......................................56
Chapter Review Exercises ...........................................................................................58

iv
Chapter 6: Modeling Random Events: The Normal and Binomial Models
Section 6.1: Probability Distributions Are Models of Random Experiments ..............65
Section 6.2: The Normal Model...................................................................................67
Section 6.3: The Binomial Model (Optional) ..............................................................79
Chapter Review Exercises ...........................................................................................81
Chapter 7: Survey Sampling and Inference
Section 7.1: Learning about the World through Surveys .............................................85
Section 7.2: Measuring the Quality of a Survey ..........................................................86
Section 7.3: The Central Limit Theorem for Sample Proportions ...............................88
Section 7.4: Estimating the Population Proportion with Confidence Intervals ...........90
Section 7.5: Comparing Two Population Proportions with Confidence......................94
Chapter Review Exercises ...........................................................................................97
Chapter 8: Hypothesis Testing for Population Proportions
Section 8.1: The Essential Ingredients of Hypothesis Testing ..................................101
Section 8.2: Hypothesis Testing in Four Steps ..........................................................102
Section 8.3: Hypothesis Tests in Detail .....................................................................107
Section 8.4: Comparing Proportions from Two Populations .....................................108
Chapter Review Exercises .........................................................................................112
Chapter 9: Inferring Population Means
Section 9.1: Sample Means of Random Samples ......................................................121
Section 9.2: The Central Limit Theorem for Sample Means .....................................122
Section 9.3: Answering Questions about the Mean of a Population..........................123
Section 9.4: Hypothesis Testing for Means ...............................................................125
Section 9.5: Comparing Two Population Means .......................................................131
Chapter Review Exercises .........................................................................................138
Chapter 10: Analyzing Categorical Variables and Interpreting Research
Section 10.1: The Basic Ingredients for Testing with Categorical Variables ............147
Section 10.2: Chi-Square Tests for Associations between
Categorical Variables ..........................................................................................149
Section 10.3: Reading Research Papers .....................................................................156
Chapter Review Exercises .........................................................................................158

1
Chapter 1: Introduction to Data
Section 1.2: Classifying and Storing Data
1.1 There are eight variables: “Female”, “Commute Distance”, “Hair Color”, “Ring Size”, “Height”, “Number of
Aunts”, “College Units Acquired”, and “Living Situation”.
1.2 There are eleven observations.
1.3 a. Living situation is categorical.
b. Commute distance is numerical.
c. Number of aunts is numerical.
1.4 a. Ring size is numerical.
b. Hair color is categorical.
c. Height is numerical.
1.5 Answers will vary but could include such things as number of friends on Facebook or foot length. Don’t copy
these answers.
1.6 Answers will vary but could include such things as class standing (“Freshman”, “Sophomore”, “Junior”, or
“Senior”) or favorite color. Don’t copy these answers.
1.7 0 = male, 1 = female. The sum represents the total number females in the data set.
1.8 There would be seven 1’s and four 0’s.
1.9 Female is categorical with two categories. The 1’s represent females, and the 0’s represent males. If you
added the numbers, you would get the number of females, so it makes sense here.
1.10 a. Freshman
b. numerical
c. categorical
1.11 a. The data is stacked.
b. 1 = male, 0 = female.
c. Male Female
1916 9802
183 153
836 1221
95
512
0
1
1
0
1
1
0
1
1
0
0

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8 Essential Statistics: Exploring the World Through Data, 3rd edition
c. No, since the sample size was fairly small; however, the difference in outcomes for treatment/control
groups may indicate that further research into the use of mindful yoga may be warranted.
1.66 a. The treatment variable was neurofeedback; the response variable is ADHD symptoms.
b. Controlled experiment (random assignment to treatment/control groups).
c. No because there were no significant differences in outcomes between any of the groups.
1.67 No. There was no control group and no random assignment to treatment or control groups.
1.68 a. Long course antibiotics: 39/238 = 16.4%; short course antibiotics: 77/229 = 33.6%.
The longer course recipients did better.
b. 10 days 5 days
Failure 39 77
Success 199 152
c. Controlled experiment (random assignment to treatment/control groups).
d. Yes. This was a controlled, randomized experiment with a large sample size.
1.69 a. LD: 8% tumors; LL: 28% tumors A greater percentage of the 24 hours of light developed tumors.
b. A controlled experiment. You can tell by the random assignment.
c. Yes, we can conclude cause and effect because it was a controlled experiment, and random assignment
will balance out potential confounding variables.
1.70 a. 43/53, or about 81.1%, of the males who were assigned to Scared Straight we rearrested. 37/55, or 67.3%, of
those receiving no treatment were rearrested. So the group from Scared Straight had a higher arrest rate.
b. No, Scared Straight does not cause a lower arrest rate because the arrest rate was higher.

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