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

British Columbia

2.90

1.77

2.5 Answers may vary. 2.6 Answers may vary. 2.7 Answers may vary. 2.8 Answers may vary. 2.9 Answers may vary.

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2.10 Response Time, 2000 21 minutes or more 16–20 minutes 11–15 minutes 6–10 minutes Less than 6 minutes

Frequency (f) 35 75 180 375 275 940

Percentage 3.72 7.98 19.15 39.89 29.26 100.00

Response Time, 2020 21 minutes or more 16–20 minutes 11–15 minutes 6–10 minutes Less than 6 minutes

Frequency (f) 45 95 155 350 250 895

Percentage 5.03 10.61 17.32 39.11 27.93 100.00

2.11 40 and Under Value 1 2 3 4 5 6

Frequency 2 2 2 1 4 4 15

Percentage 13.33 13.33 13.33 6.67 26.67 26.67 100.00

Cumulative Percentage 13.33 26.66 39.99 46.66 73.33 100.00

Over 40 Value 1 2 3 4 5 6 7 8

Frequency 1 4 2 2 1 0 3 3 16

Percentage 6.25 25.00 12.50 12.50 6.25 0.00 18.75 18.75 100.00

Cumulative Percentage 6.25 31.25 43.75 56.25 62.50 62.50 81.25 100.00

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DETAILED SOLUTION TO SELECTED TEXT PROBLEMS 2.2 a. Social science majors = 97 + 132 = 229 Male social science majors = 97 % of social science majors who are male: f     100 n  97     100  229   0.4236  100  42.36% b. Business majors = 156 + 139 = 295 Female business majors = 139 Proportion of business majors who are female: f  n 139  295  0.47 c. For humanities: Number of males = 114 Number of females = 83 Ratio of males to females:

2.3 Homicide rate: Number of homicides = 13 Population = 211,732

(

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WHAT CAN I DO IN CLASS? 1. Pass out a sheet of paper in class and have students write down their gender and the academic school year in which they are currently enrolled. Display the results for the entire class and have students decide what type of distribution would best depict the results. For example: Gender Female Female Male Other Male Other Male Female Male Female Female Other Female Female Other Female Female Male Female Male

Academic Year 1 2 1 3 2 1 1 1 2 3 3 4 2 1 1 1 2 2 1 3

Provide students with a column of intervals and have them write out the real limits and midpoints for each interval. This will help familiarize them with statistical definitions.

Class Interval 17–18 15–16

Frequency 7 15

Real Limits 16.5–18.5 14.5–16.5

Therefore, when we subtract the real lower limit from the real upper limit, we get the actual width of the interval, which in this case is 2.