Lecture Slides Elementary Statistics Eleventh Edition and the

Lecture Slides Elementary Statistics Eleventh Edition and the Triola Statistics Series by Mario F. Triola Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 1

Chapter 15 Projects, Procedures, Perspectives 15 -1 Projects 15 -2 Procedures 15 -3 Perspectives Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 2

Section 15 -1 Projects Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 3

Key Concept This section includes suggestions for a final project in the introductory statistics course. One fantastic advantage of this course is that it deals with skills and concepts that can be applied immediately to the real world. After only one semester, students are able to conduct their own studies. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 4

Projects v Group/Individual Topics can be assigned to individuals, but group projects are particularly effective because they help develop the interpersonal skills that are so necessary in today’s working environment. v Oral Report A 10 - to 15 -minute-long class presentation should involve all group members in a coordinated effort to clearly describe the important components of the study. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 5

Projects v Written Report A brief written report should include the following: 1. List of data collected along with description of how the data were obtained. 2. Description of the method of analysis. 3. Relevant graphs and/or statistics, including STATDISK, Minitab, Excel, or TI-83/84 displays. 4. Statement of conclusions. 5. Reasons why the results might not be correct, along with a description of ways in which the study could be improved, given sufficient time and money. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 6

Projects v Large Classes or Online Classes: Posters or Power. Point Some classes are too large for individual projects or group projects with three or four or five students per group. Some online classes are not able to meet as a group. For such cases, reports of individual or small group projects can be presented through posters or Power. Point presentations. v Project Topics The “Cooperative Group Activities” listed near the end of each chapter include more than 100 suggestions for projects. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 7

Projects v Surveys can be an excellent source of data. 1. When people “randomly” select digits (as in Question 2), are the results actually random? 2. Do the last four digits of social security numbers appear to be random? 3. Do males and females carry different amounts of change? 4. Do males and females have different numbers of credit cards? 5. Is there a difference in pulse rates between those who exercise and those who do not? Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 8

Projects v Surveys can be an excellent source of data. 6. Is there a difference in pulse rates between those who smoke and those who do not? 7. Is there a relationship between exercise and smoking? 8. Is there a relationship between eye color and exercise? 9. Is there a relationship between exercise and the number of hours worked each week? 10. Is there a correlation between height and pulse rate? Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 9

Section 15 -2 Procedures Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 10

Key Concept This section describes a general procedure for conducting a statistical analysis of data. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 11

Procedures v Context, Source, Sampling Method Instead of mindlessly plugging data into some particular statistical procedure, we should begin with some basic considerations, including these: 1. Clearly identify the context of the data. 2. Consider the source of the data and determine whether that source presents any issues of bias that might affect the validity of the data. 3. Consider the sampling method to ensure that it is the type of sampling likely to result in data that are representative of the population. Be especially wary of voluntary-response samples. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 12

Procedures v Exploring, Comparing, Describing After collecting data, address the following: 1. Center: Find the mean and median. 2. Variation: Find the range and standard deviation. 3. Distribution: Construct a histogram and a normal quantile plot. 4. Outliers: Identify any sample values that lie very far away from the vast majority of the others. 5. Time: Determine if the population is stable or if its characteristics are changing over time. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 13

Procedures v Inferences: Estimating Parameters and Hypothesis Testing Here are some key questions that should be answered: • What is the level of measurement (nominal, ordinal, interval, ratio) of the data? • Does the study involve one, two, or more populations? • What is the relevant parameter (mean, standard deviation, proportion)? • Is the population standard deviation known? • Is there reason to believe that the population is normally distributed? • What is the basic question or issue to address? Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 14

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Ordinal (such as data consisting of ranks) Nominal (data consisting of proportions or frequency counts for different categories) Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 15

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement One Population Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Number of Populations Two Populations More than Two Populations Chap. 12, 13 -5 Ordinal (such as data consisting of ranks) Nominal (data consisting of proportions or frequency counts for different categories) Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 16

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement Claim or Parameter Mean One Population Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Number of Populations Variance Two Populations More than Two Populations Chap. 12, 13 -5 Ordinal (such as data consisting of ranks) Nominal (data consisting of proportions or frequency counts for different categories) Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 17

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement Claim or Parameter Mean One Population Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Number of Populations Variance Two Populations Means: 9 -3, 9 -4 More than Two Populations Chap. 12, 13 -5 Variances: 9 -5 Correlation, Regression Chap. 10, 13 -6 Ordinal (such as data consisting of ranks) Nominal (data consisting of proportions or frequency counts for different categories) Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 18

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement Claim or Parameter Mean One Population Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Number of Populations Variance Two Populations Means: 9 -3, 9 -4 More than Two Populations Chap. 12, 13 -5 Variances: 9 -5 Inference Estimating with Confidence Interval: 7 -3, 7 -4 Hypothesis Testing with Large Sample: 8 -4, 8 -5 Correlation, Regression Chap. 10, 13 -6 Ordinal (such as data consisting of ranks) Nominal (data consisting of proportions or frequency counts for different categories) Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 19

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement Claim or Parameter Mean One Population Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Number of Populations Variance Two Populations Means: 9 -3, 9 -4 More than Two Populations Chap. 12, 13 -5 Variances: 9 -5 Ordinal (such as data consisting of ranks) Correlation, Regression Chap. 10, 13 -6 Inference Estimating with Confidence Interval: 7 -3, 7 -4 Hypothesis Testing with Large Sample: 8 -4, 8 -5 Estimating with Confidence Interval: 7 -5 Hypothesis Testing: 8 -6 Nominal (data consisting of proportions or frequency counts for different categories) Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 20

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement Claim or Parameter Mean One Population Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Number of Populations Ordinal (such as data consisting of ranks) Variance Two Populations Means: 9 -3, 9 -4 More than Two Populations Chap. 12, 13 -5 Variances: 9 -5 One Population 13 -2 Correlation, Regression Chap. 10, 13 -6 Inference Estimating with Confidence Interval: 7 -3, 7 -4 Hypothesis Testing with Large Sample: 8 -4, 8 -5 Estimating with Confidence Interval: 7 -5 Two Populations More than Two Populations 13 -5 Hypothesis Testing: 8 -6 Nominal (data consisting of proportions or frequency counts for different categories) Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 21

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement Claim or Parameter Mean One Population Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Number of Populations Ordinal (such as data consisting of ranks) Variance Two Populations Means: 9 -3, 9 -4 More than Two Populations Chap. 12, 13 -5 Variances: 9 -5 One Population 13 -2 Two Populations More than Two Populations 13 -5 Correlation, Regression Chap. 10, 13 -6 Inference Estimating with Confidence Interval: 7 -3, 7 -4 Hypothesis Testing with Large Sample: 8 -4, 8 -5 Estimating with Confidence Interval: 7 -5 Independent: 13 -4 Matched Pairs: 13 -3 Hypothesis Testing: 8 -6 Nominal (data consisting of proportions or frequency counts for different categories) Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 22

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement Claim or Parameter Mean One Population Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Number of Populations Ordinal (such as data consisting of ranks) Two Populations Means: 9 -3, 9 -4 More than Two Populations Chap. 12, 13 -5 Variances: 9 -5 One Population 13 -2 Two Populations More than Two Populations 13 -5 Nominal (data consisting of proportions or frequency counts for different categories) Variance Correlation, Regression Chap. 10, 13 -6 Inference Estimating with Confidence Interval: 7 -3, 7 -4 Hypothesis Testing with Large Sample: 8 -4, 8 -5 Estimating with Confidence Interval: 7 -5 Independent: 13 -4 Matched Pairs: 13 -3 Hypothesis Testing: 8 -6 Frequency Counts for Categories Proportions Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 23

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement Claim or Parameter Mean One Population Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Number of Populations Ordinal (such as data consisting of ranks) Two Populations Means: 9 -3, 9 -4 More than Two Populations Chap. 12, 13 -5 Variances: 9 -5 One Population 13 -2 Two Populations More than Two Populations 13 -5 Nominal (data consisting of proportions or frequency counts for different categories) Variance Frequency Counts for Categories Correlation, Regression Chap. 10, 13 -6 Inference Estimating with Confidence Interval: 7 -3, 7 -4 Hypothesis Testing with Large Sample: 8 -4, 8 -5 Estimating with Confidence Interval: 7 -5 Independent: 13 -4 Matched Pairs: 13 -3 Hypothesis Testing: 8 -6 Multinomial (one row) 11 -2 Contingency Table (multiple rows, columns) 11 -3 Proportions Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 24

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement Claim or Parameter Mean One Population Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Number of Populations Ordinal (such as data consisting of ranks) Two Populations Means: 9 -3, 9 -4 More than Two Populations Chap. 12, 13 -5 Variances: 9 -5 One Population 13 -2 Two Populations More than Two Populations 13 -5 Nominal (data consisting of proportions or frequency counts for different categories) Variance Frequency Counts for Categories Proportions Correlation, Regression Chap. 10, 13 -6 Inference Estimating with Confidence Interval: 7 -3, 7 -4 Hypothesis Testing with Large Sample: 8 -4, 8 -5 Estimating with Confidence Interval: 7 -5 Independent: 13 -4 Matched Pairs: 13 -3 Hypothesis Testing: 8 -6 Multinomial (one row) 11 -2 Contingency Table (multiple rows, columns) 11 -3 Two Populations: 9 -2 One Population Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 25

FIGURE 15 -1 Selecting the Appropriate Procedure Level of Measurement Claim or Parameter Mean One Population Interval or Ratio (such as heights, weights) What is the level of measurement of the data? 1 -2 Number of Populations Ordinal (such as data consisting of ranks) Two Populations Means: 9 -3, 9 -4 More than Two Populations Chap. 12, 13 -5 Variances: 9 -5 One Population 13 -2 Two Populations More than Two Populations 13 -5 Nominal (data consisting of proportions or frequency counts for different categories) Variance Frequency Counts for Categories Proportions Correlation, Regression Chap. 10, 13 -6 Estimating with Confidence Interval: 7 -3, 7 -4 Hypothesis Testing with Large Sample: 8 -4, 8 -5 Estimating with Confidence Interval: 7 -5 Independent: 13 -4 Matched Pairs: 13 -3 Hypothesis Testing: 8 -6 Multinomial (one row) 11 -2 Contingency Table (multiple rows, columns) 11 -3 Two Populations: 9 -2 One Population Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Inference Estimating Proportion with Confidence Interval: 7 -2 Hypothesis Testing: 8 -3, 13 -2 15. 1 - 26

Procedures v Conclusions and Practical Implications After completing the statistical analysis: • we should state conclusions in a way that is clear to those unfamiliar with statistics and its terminology • we should carefully avoid making statements not justified by the statistical analysis (such as using a correlation to conclude that one variable is the cause of the other) • we should identify practical implications of the results Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 27

Section 15 -3 Perspectives Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 28

Key Concept No single introductory statistics course can transform anyone into an expert statistician. Know that professional help is available from expert statisticians, and this introductory statistics course will help you in discussions with one of these experts. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 29

Perspective v Successful completion of an introductory statistics course results in benefits far beyond the attainment of credit toward a college degree. • Improved job marketability • Ability to critically analyze reports in media and journals • Understanding of the basic concepts of probability and chance • Know to consider context, source and sampling methods Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 30

Perspective • Know to investigate measures of center (mean and median), variation (range and standard deviation), distribution (frequency distribution or graph), presence of outliers, whether the population is table or changing over time • Know and understand importance of estimating population parameters (mean, standard deviation, and proportion) as well as testing claims about population parameters Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 31

Perspective v Remember that expert ability in analyzing statistics is of little value if good sampling techniques are not employed to develop the sample. v Although computers and calculators are good at yielding results, careful interpretation of the results are required. v Successful completion of an introductory statistics course can enable students to grow as individuals and professionals and become people who are truly educated. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 15. 1 - 32