2026
STATISTICS II
SOLUTIONS MANUAL
KOEN HANEGREEFS
VUB
,Table of Contents
Statistics II — Worked Solutions Manual ......................................................................... 4
How to use this manual............................................................................................... 4
Chapter 10 — Worked Solutions (WPO 2: Confidence Intervals for Proportions) ................ 5
Exercise 4 — Women in Latvia ..................................................................................... 5
Exercise 5 — Store Customers .................................................................................... 6
Exercise 34 — Mortgages 2013 .................................................................................... 6
Exercise 35 — Loans ................................................................................................... 7
Exercise 71 — Smartphones ........................................................................................ 8
Exercise 75 — Pilot Study (Emissions) .......................................................................... 9
RStudio Exercise — Holiday Shopping ......................................................................... 9
LEGO Example — Summary (Conceptual Illustration) ................................................. 10
Chapter 11 — Worked Solutions (WPO 3: Confidence Intervals for Means)...................... 12
Exercise 24 — Confidence Intervals and Sample Size ................................................. 12
Exercise 29 — Parking Garage ................................................................................... 13
Exercise 36 — Late Flight Arrivals............................................................................... 14
Exercise 41 — Wire Manufacturing............................................................................. 14
Exercise 47 (R Studio) — Credit Card Spending .......................................................... 15
Chapter 12 — Worked Solutions (WPO 4: Testing Hypotheses About Proportions) ........... 17
Exercise 11 — Pizza (p-value interpretation) (At home)................................................ 17
Exercise 15 — Setting Up Hypotheses (At home) ........................................................ 17
Exercise 33 — Twins (In class) ................................................................................... 18
Exercise 27 — Absentees (In class) ............................................................................ 19
Exercise R Studio — Flower Hill Real Estate (In class) ................................................. 20
Chapter 13 — Worked Solutions (WPO 5: More About Tests & Intervals (paired t-test,
errors, power)) ............................................................................................................. 23
Exercise 27 — Loans (at home) (Important) ................................................................ 23
Exercise 29 — Second Loan (at home) (Important)...................................................... 24
Exercise 33 — Testing Cars (Important) ...................................................................... 24
Exercise 37 — Gender Discrimination (Important) ...................................................... 25
Exercise 47 — Two Coins (Neutral) ............................................................................ 26
R Exercise — Flower Hill (Important) .......................................................................... 27
Chapter 14 — Worked Solutions (WPO 6: Comparing Two Means) .................................. 30
Koen Hanegreefs 1
, Exercise 26 — Sports (at home) ................................................................................. 30
Exercise 32 — Soccer................................................................................................ 31
Exercise 34 — Living Cost .......................................................................................... 31
Exercise 55 — Income (at home)................................................................................ 33
R Studio Exercise — CardioX Drug Trial ...................................................................... 33
Chapter 15 — Worked Solutions (WPO 7: Chi-Square Tests) ........................................... 36
Exercise 25 — Cranberry Juice (Homogeneity) (Important) .......................................... 36
Exercise 32 — Labour Force Immigration (Homogeneity / 2×2) (Important) .................. 38
Exercise 41 — Racial Steering (Independence) (Important) ......................................... 40
Exercise 43 — Racial Steering Revisited: Confidence Interval (Important) .................... 41
R Studio Exercise — New Drug (CardioX vs StandardCare) (Neutral) ............................ 42
Question 1: Do severe side effects differ across hospitals (site)? ................................ 42
Question 2: Do severe side effects differ by drug? ...................................................... 42
LEGO Example — Chi-Square Test of Independence with Expected Count Problem
(Neutral)................................................................................................................... 43
Chapter 16 — Worked Solutions (WPO 8: Linear Regression) .......................................... 45
Exercise: WPO 8 Part 1 — Elderly Care Survey (Q5: Regression) (Important)................. 45
Exercise 30 (At Home) — Automobiles (Important) ..................................................... 46
Exercise 37 — Labor Productivity 2020 (Important) ..................................................... 47
Exercise 39 — Labor Productivity 2020, Part 2 (Important) .......................................... 48
Exercise 56 — Youth Employment 2016 (Important).................................................... 48
R Studio Exercise — Graduate Employment (Important) ............................................. 49
LEGO Example — Full Worked Regression Pipeline (Neutral) ...................................... 50
Chapter 17 — Worked Solutions (WPO 9: Inference for Regression & Residual Analysis) .. 53
Exercise 12 — Durbin-Watson for Mail Orders (Important) .......................................... 53
Exercise 21 — Palm Oil Prices (Scatterplot Interpretation) (Important) ........................ 53
Exercise 32 — Unusual Points in Scatterplots (Important) ........................................... 54
Exercise 40 — Palm Oil Part 2: Price Difference Regression (Important) ....................... 55
Exercise 53 — Lobster Catch Value 1950–2016 (Important) ........................................ 56
R Exercise — Energy Consumption at a Belgian Factory (Important) ............................ 57
Summary Table (Important) ....................................................................................... 61
Chapter 23 — Worked Solutions (Seminar 10: Non-Parametric Methods)........................ 62
Exercise 6 — Choosing the Right Test (Important) ....................................................... 62
Koen Hanegreefs 2
, Exercise 17 — Trophy Sizes (Mann-Whitney) (Important) ............................................. 62
Exercise 22 — Scanner Errors (Wilcoxon Signed-Rank) (Important) ............................. 63
Exercise 26 — Cholesterol Drugs (Kruskal-Wallis) (Important) .................................... 63
Exercise 30 — Carbon Footprint (Spearman’s 𝜌) (Neutral) .......................................... 64
23.9 What Can Go Wrong (Important) ........................................................................ 65
Koen Hanegreefs 3
STATISTICS II
SOLUTIONS MANUAL
KOEN HANEGREEFS
VUB
,Table of Contents
Statistics II — Worked Solutions Manual ......................................................................... 4
How to use this manual............................................................................................... 4
Chapter 10 — Worked Solutions (WPO 2: Confidence Intervals for Proportions) ................ 5
Exercise 4 — Women in Latvia ..................................................................................... 5
Exercise 5 — Store Customers .................................................................................... 6
Exercise 34 — Mortgages 2013 .................................................................................... 6
Exercise 35 — Loans ................................................................................................... 7
Exercise 71 — Smartphones ........................................................................................ 8
Exercise 75 — Pilot Study (Emissions) .......................................................................... 9
RStudio Exercise — Holiday Shopping ......................................................................... 9
LEGO Example — Summary (Conceptual Illustration) ................................................. 10
Chapter 11 — Worked Solutions (WPO 3: Confidence Intervals for Means)...................... 12
Exercise 24 — Confidence Intervals and Sample Size ................................................. 12
Exercise 29 — Parking Garage ................................................................................... 13
Exercise 36 — Late Flight Arrivals............................................................................... 14
Exercise 41 — Wire Manufacturing............................................................................. 14
Exercise 47 (R Studio) — Credit Card Spending .......................................................... 15
Chapter 12 — Worked Solutions (WPO 4: Testing Hypotheses About Proportions) ........... 17
Exercise 11 — Pizza (p-value interpretation) (At home)................................................ 17
Exercise 15 — Setting Up Hypotheses (At home) ........................................................ 17
Exercise 33 — Twins (In class) ................................................................................... 18
Exercise 27 — Absentees (In class) ............................................................................ 19
Exercise R Studio — Flower Hill Real Estate (In class) ................................................. 20
Chapter 13 — Worked Solutions (WPO 5: More About Tests & Intervals (paired t-test,
errors, power)) ............................................................................................................. 23
Exercise 27 — Loans (at home) (Important) ................................................................ 23
Exercise 29 — Second Loan (at home) (Important)...................................................... 24
Exercise 33 — Testing Cars (Important) ...................................................................... 24
Exercise 37 — Gender Discrimination (Important) ...................................................... 25
Exercise 47 — Two Coins (Neutral) ............................................................................ 26
R Exercise — Flower Hill (Important) .......................................................................... 27
Chapter 14 — Worked Solutions (WPO 6: Comparing Two Means) .................................. 30
Koen Hanegreefs 1
, Exercise 26 — Sports (at home) ................................................................................. 30
Exercise 32 — Soccer................................................................................................ 31
Exercise 34 — Living Cost .......................................................................................... 31
Exercise 55 — Income (at home)................................................................................ 33
R Studio Exercise — CardioX Drug Trial ...................................................................... 33
Chapter 15 — Worked Solutions (WPO 7: Chi-Square Tests) ........................................... 36
Exercise 25 — Cranberry Juice (Homogeneity) (Important) .......................................... 36
Exercise 32 — Labour Force Immigration (Homogeneity / 2×2) (Important) .................. 38
Exercise 41 — Racial Steering (Independence) (Important) ......................................... 40
Exercise 43 — Racial Steering Revisited: Confidence Interval (Important) .................... 41
R Studio Exercise — New Drug (CardioX vs StandardCare) (Neutral) ............................ 42
Question 1: Do severe side effects differ across hospitals (site)? ................................ 42
Question 2: Do severe side effects differ by drug? ...................................................... 42
LEGO Example — Chi-Square Test of Independence with Expected Count Problem
(Neutral)................................................................................................................... 43
Chapter 16 — Worked Solutions (WPO 8: Linear Regression) .......................................... 45
Exercise: WPO 8 Part 1 — Elderly Care Survey (Q5: Regression) (Important)................. 45
Exercise 30 (At Home) — Automobiles (Important) ..................................................... 46
Exercise 37 — Labor Productivity 2020 (Important) ..................................................... 47
Exercise 39 — Labor Productivity 2020, Part 2 (Important) .......................................... 48
Exercise 56 — Youth Employment 2016 (Important).................................................... 48
R Studio Exercise — Graduate Employment (Important) ............................................. 49
LEGO Example — Full Worked Regression Pipeline (Neutral) ...................................... 50
Chapter 17 — Worked Solutions (WPO 9: Inference for Regression & Residual Analysis) .. 53
Exercise 12 — Durbin-Watson for Mail Orders (Important) .......................................... 53
Exercise 21 — Palm Oil Prices (Scatterplot Interpretation) (Important) ........................ 53
Exercise 32 — Unusual Points in Scatterplots (Important) ........................................... 54
Exercise 40 — Palm Oil Part 2: Price Difference Regression (Important) ....................... 55
Exercise 53 — Lobster Catch Value 1950–2016 (Important) ........................................ 56
R Exercise — Energy Consumption at a Belgian Factory (Important) ............................ 57
Summary Table (Important) ....................................................................................... 61
Chapter 23 — Worked Solutions (Seminar 10: Non-Parametric Methods)........................ 62
Exercise 6 — Choosing the Right Test (Important) ....................................................... 62
Koen Hanegreefs 2
, Exercise 17 — Trophy Sizes (Mann-Whitney) (Important) ............................................. 62
Exercise 22 — Scanner Errors (Wilcoxon Signed-Rank) (Important) ............................. 63
Exercise 26 — Cholesterol Drugs (Kruskal-Wallis) (Important) .................................... 63
Exercise 30 — Carbon Footprint (Spearman’s 𝜌) (Neutral) .......................................... 64
23.9 What Can Go Wrong (Important) ........................................................................ 65
Koen Hanegreefs 3
