Instructor Solution Manual For Statistics A Tool for Social Research and Data Analysis, 5th Edition by welldoneassistant

TABLE OF CONTENTS Preface.............................................................................................................................. iv Chapter 1: Introduction .................................................................................................. 1-1 Chapter 2: Basic Descriptive Statistics: Percentages, Ratios and Rates, Tables, Charts, and Graphs ......................................................................................................... 2-1 Chapter 3: Measures of Central Tendency and Dispersion ........................................... 3-1 Chapter 4: The Normal Curve........................................................................................ 4-1 Chapter 5: Introduction to Inferential Statistics: Sampling and the Sampling Distribution .................................................................................................... 5-1 Chapter 6: Estimation Procedures for Sample Means and Proportions ......................... 6-1 Chapter 7: Hypothesis Testing with Nominal and Ordinal Variables: Chi Square ....... 7-1 Chapter 8: Measures of Association for Variables Measured at the Nominal Level..... 8-1 Chapter 9: Measures of Association for Variables Measured at the Ordinal Level ...... 9-1 Chapter 10: Hypothesis Testing with Means and Proportions: The One-Sample Case.................................................................................................. 10-1 Chapter 11: Hypothesis Testing with Means and Proportions: The Two-Sample Case ................................................................................................. 11-1 Chapter 12: Hypothesis Testing with More Than Two Means: One-Way Analysis of Variance ................................................................................................................... 12-1 Chapter 13: Hypothesis Testing and Measures of Association for Variables Measured at the Interval-Ratio Level ........................................................................................... 13-1 Chapter 14: Partial Correlation and Multiple Regression and Correlation .................. 14-1

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CHAPTER 1 INTRODUCTION SUMMARY Statistics: A Tool for Social Research, Fifth Canadian Edition, begins by explaining the role of statistics in the research process. The discussion is guided by ―The Wheel of Science,‖ as conceptualized by Walter Wallace (Figure 1.1). The text consistently presents statistics in the context of the research enterprise; that is, statistics are always presented not as ends in themselves, but as useful devices or tools for answering questions and testing theories. The chapter also distinguishes between descriptive and inferential statistics, and between univariate, bivariate, and multivariate statistics. The distinction between discrete and continuous variables and the concept of level of measurement are presented as well. The latter is stressed throughout the text as an organizational device and as a major criterion for selecting statistics appropriately. Exercises are provided at the end of the chapter for reviewing the characteristics of the three levels of measurement used in this text.

NEW TO THE FIFTH CANADIAN EDITION The ―You are the Researcher‖ section has been updated with new survey data, the 2018 GSS and CCHS.

WHAT CAN I DO IN CLASS? 1. Provide students with a table consisting of a variable (Column 1), the variable’s response categories (Column 2), whether it is independent or dependent (Column 3), and the level of measurement (Column 4). Ask students to identify the variables as independent or dependent, as well as the level of measurement for each given variable. Go over the answers in class. For example, gender is an independent nominal-level variable and health is a dependent variable measured at either the interval-ratio (body weight in kilograms), ordinal (poor, good, or excellent self-rated health), or nominal (have a family doctor, yes or no) level. 2. Show a list of examples of populations and samples, and have students identify each as such. For example, we want to know if more male students or more female students visit the local pub on campus in a given week. a. Sample: The number of male and female visitors you observe visiting during a one-hour period b. Population: Everyone who visits the local pub on campus in a given week

WHAT CAN I DO ONLINE? 1. Have students look up examples online of variables that can be identified as having more than one level of measurement, depending on how they are categorized. For example, household income can be reported as a continuous variable or grouped into finite categories (see, for example, https://www150.statcan.gc.ca/n1/en/catalogue/98-400-X2016097). 2. Have students search a recent news story or report online and identify and list variables that could be used to conduct a quantitative analysis (see, for example, Angus Reid Institute’s report on term care facilities in Canada during the COVID19 pandemic, https://angusreid.org/long-term-care-covid/).

CHAPTER 2 BASIC DESCRIPTIVE STATISTICS Percentages, Ratios and Rates, Tables, Charts, and Graphs SUMMARY This chapter covers relatively simple descriptive devices: percentages and proportions, ratios, rates, frequency distributions, pie and bar charts, histograms, and frequency polygons. The emphasis is on frequency distributions and the construction and interpretation of these tables for variables measured at each of the three different levels. Instructors may want to supplement this material with additional examples of each technique and/or graphs and charts, especially those created by software such as Microsoft Excel. The underlying theme of this chapter is the need to present results clearly, to communicate results accurately and concisely but without losing too much detail. The problem used in Section 2.6: Charts and Graphs, for example, is intended to contrast the anarchy of raw, unorganized data with the clarity and simplicity of frequency distributions and various graphs.

NEW TO THE FIFTH CANADIAN EDITION Most tables, graphs, and application boxes have been updated to better reflect the underlying relevance and importance of using basic descriptive statistics to help understand society. The SPSS exercises have been updated with the new Canadian survey data used in the textbook.

a. Complex A: (5/20) × 100 = 25.00% Complex B: (10/20) × 100 = 50.00% b. Complex A: 4:5 = 0.80 Complex B: 6:10 = 0.60 c. Complex A: (0/20) = 0.00 Complex B: (1/20) = 0.05 d. (6/(4 + 6)) = (6/10) = 60.00% e. Complex A: 8:5 = 1.60 Complex B: 2:10 = 0.20

2.2 a. 42.36% (see below for detailed solution) b. 0.47 (see below for detailed solution c. 1.37 (see below for detailed solution) d. 51.83% e. 0.03 f. 0.08 g. 25.47% h. 0.68 i. 4.34 j. 0.03

2.3 Bank robbery rate = (47/211,732) × 100,000 = 22.20 Homicide rate = (13/211,732) × 100,000 = 6.14 Auto theft rate = (23/211,732) × 100,000 = 10.86

2.4 State New Jersey Iowa Alabama Texas California

1997 4.20 1.82 10.29 6.83 7.99

2019 3.23 2.54 11.97 5.92 4.54

Province Nova Scotia Quebec Ontario Manitoba

1997 2.56 1.80 1.56 2.72

2019 0.62 0.91 1.69 5.26

ANSWERS TO TEXT PROBLEMS 4.1 Xi

Z score

5 6 7 8 9 11 12 14 15 16 18

–1.67 –1.33 –1.00 –0.67 –0.33 0.33 0.67 1.33 1.67 2.00 2.67

% Area Above 95.25 90.82 84.13 74.86 62.93 37.07 25.14 9.18 4.75 2.28 0.38

% Area Below 4.75 9.18 15.87 25.14 37.07 62.93 74.86 90.82 95.25 97.72 99.62

4.2 Z score 1.50 –1.00 –1.25

0.86 –0.63 0.26 1.21 –0.02 0.17 –1.02

% Area Above 6.68 84.13 89.44 19.49 73.57 39.74 11.31 50.80 43.25 84.61

% Area Below 93.32 (see below for detailed solution) 15.87 (see below for detailed solution) 10.56 80.51 26.43 60.26 88.69 49.20 56.75 15.39

4.3 a. b. c. d. e. f. g. h. i. j.

Z scores 0.10 & 1.10 0.60 & 1.10 0.60 0.90 0.60 & –0.40 0.10 & –0.40 0.10 0.30 0.60 1.10

Area (%) 32.45 13.86 27.43 18.41 38.11 19.52 53.98 61.79 72.57 86.43

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4.4 a. 22.34% (see below for detailed solution) d. 86.64% e. 1.39% f. 5.74%

b. 61.79% g. 19.34%

c. 61.79% h. 34.62%

4.5 Xi

Z Score

60 57 55 67 70 72 78 82 90 95

−2.00 −2.50 −2.83 −0.83 −0.33 20.00 21.00 21.67 23.00 23.83

Number of Retirees Above 195 199 199 159 126 100 32 10 1 1

Number of Retirees Below 5 1 1 41 74 100 168 190 199 199

Note: Number of retirees (a discrete variable) has been rounded off to the nearest whole number.

4.6 a. 5.05% f. 41.69% k. 60.64%

b. 23.27% g. 70.67% l. 88.10%

c. 57.14% h. 29.07%

d. 86.21% i. 2.81%

e. 6.85% j. 15.87%

4.7 a. b. c. d. e. f.

Z score −2.20 1.80 −0.20 & 1.80 0.80 & 2.80 −1.20 0.80

4.8 a. Xi = 27 days

Area (%) 1.39 96.41 54.34 20.93 88.49 21.19

b. Xi = 24 days

c. Xi = 21 days

4.9 a. b. c. d. e.

Z Scores −1.00 & 1.50 0.25 & 1.50 1.50 0.25 & −2.25 −1.00 & −2.25

Area 0.7745 0.3345 0.0668 0.5865 0.1465

4.10 With a Z score of –0.39 (corresponding as closely as possible to an area between the mean and Z of 0.1500); a. Xi = 980.50 b. Xi = 96.10 4.11 With a Z score of 0.00 (corresponding to an area between the mean and Z of 0.0000) a. Xi = 1000.00 b. Xi = 100.00 4.12 a. 0.1112 e. 0.6711

b. 0.4129 f. 0.3694

c. 0.2177 g. 0.1174

d. 0.0375

4.13 The probability of finding a score greater than 80, when the mean is 65 and the standard deviation is 15, is 0.1587. 4.14

0.0359

4.15

Yes. The raw score of 110 translates into a Z score of +2.88. 99.80% of the area lies below this score, so this individual was in the top 1% on this test.

4.16

Social worker: Z = +0.53 Employment counsellor: Z = +0.67

4.17

For the ﬁrst event, the probability is 0.0919, and for the second, the probability is 0.0655. The ﬁrst event is more likely.

4.18

GPA 3.20 3.21 3.25 3.30 3.35

Z score 1.27 1.30 1.42 1.58 1.73

Area Below (%) 89.80 90.32 92.22 94.29 95.82

Only the 3.20 GPA is not in the top 10%.

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DETAILED SOLUTIONS TO SELECTED TEXT PROBLEMS 4.2 For Xi = 650,

Z

Xi  X 650  500   1.50 s 100

The area between the score and the mean is 43.32%, so the area below = 50.00% + 43.32% = 93.32%. The ―area beyond‖ (or area above a positive Z score) is 6.68%. For Xi = 400,

Z

Xi  X 400  500   1.00 s 100

The area between the score and the mean is 34.13%, so the area above = 50.00% + 34.13% = 84.13%. The ―area beyond‖ (or area below a negative Z score) is 15.87.

4.4 a. For Xi = 40,

Z

Xi  X 40  50   1.00 s 10

Z

Xi  X 47  50   0.30 s 10

For Xi = 47,

Areas between scores and mean: For Z = –1.00, area = 0.3413 For Z = –0.30, area = 0.1179 Area between scores: (0.3413) – (0.1179) = 0.2234

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WHAT CAN I DO IN CLASS? 1. Provide students with several different Z scores and have them draw the area depicted by these scores using a Z table. Go over the answers in class. For example, find the area between a positive Z score (Z = 0.45) and a negative Z score (Z = –2.13). 2. Hand out a drawing of a theoretical normal curve and have students fill out the percentages and standard deviations. Ensure they understand the symmetrical nature of the curve.

WHAT CAN I DO ONLINE? 1. Using the Khan Academy website, ask students to practice calculating z-scores: https://www.khanacademy.org/math/ap-statistics/density-curves-normaldistribution-ap/measuring-position/e/z_scores_1 2. Ask students to use http://www.mathcracker.com/normal_probability.php to compute a normal probability distribution.

CHAPTER 5 INTRODUCTION TO INFERENTIAL STATISTICS Sampling and the Sampling Distribution SUMMARY This chapter begins with a brief overview of probability sampling techniques, but the primary goal is to familiarize students with the concept of the sampling distribution and

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its relationship to samples and populations. This concept is, of course, both difficult for students and crucial for an understanding of inferential statistics. The chapter is designed to provide a more tangible understanding of this concept by demonstrating, in Section 5.4, the construction and final shape of a sampling distribution. There is also an exercise at the end of the chapter for constructing a sampling distribution.

NEW TO THE FIFTH CANADIAN EDITION Section 5.3 demonstrates the Central Limit Theorem in ―action,‖ or how the sampling distribution changes with sample size. A new section, 5.5, on the sampling distribution of proportions has been added. It explains and shows how the normal sampling distribution can be extended to nominal- or ordinal-level variables using proportions instead of means.

ANSWERS TO TEXT PROBLEMS 5.1 a–d. Answers may vary.

WHAT CAN I DO IN CLASS? 1. Provide students with a list representing examples of populations and samples and have them label the examples as either representing a population or a sample. For example, all registered voters in the GTA, number of voters who voted: Liberal, Conservative, NDP, or other. 2. Have students list consequences of not having a representative random sample. For example, use the rule of EPSEM.

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