June 7, 2019

CHAPTER 12

Generalizing Your Findings

LEARNING OBJECTIVES

To find out what it means to generalize the findings of a survey

To understand that a sample finding is used to estimate a population fact

To discover how to estimate a confidence interval for a percentage or an average

To learn how to test a hypothesis about a population percentage or an average

To become familiar with the “Generalize” functions of the XL Data Analyst

CHAPTER OUTLINE

Generalizing a Sample’s Findings

Estimating the Population Value

How to Estimate a Population Percentage (Categorical Data)

Calculating a Conference Interval for a Percentage

Interpreting a 95% Confidence Interval for a Percentage

How to Obtain a 95% Confidence Interval for a Percentage with XL Data Analyst

How to Estimate a Population Average (Metric Data)

Calculating a Confidence Interval for an Average

Interpreting a Confidence Interval for an Average

How to Obtain a 95% Confidence Interval for an Average with XL Data Analyst

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Flow Chart of Generalization Analysis for Confidence Intervals

Testing Hypotheses About Percents of Averages

Testing a Hypothesis About a Percentage

Why Use the 95% Significance Level?

How Do We Know That We Have Made the Correct Decision?

Testing a Directional Hypothesis

How to Test a Hypothesis About a Percentage with XL Data Analyst

Is It t or z? And Why You Do Not Need to Worry About It

Testing a Hypothesis About an Average

How to Test a Hypothesis About an Average with XL Data Analyst

Interpreting Your Hypothesis Test

Flow Chart of Generalization Analysis for Hypothesis Tests

How to Present Generalization Analyses

Guidelines for Confidence Intervals

The General Case

The Findings-Specific Case

Guidelines for Hypothesis Tests

KEY TERMS

Confidence interval

Directional hypothesis

Generalization

Parameter

“Parameter estimation”

Population fact

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Hypothesis

Hypothesis testing

Intuitive hypothesis testing

Most commonly used level of confidence

Null hypothesis

Sample finding

Sampling distribution

Standard error

Standard error of a percentage

Standard error of the average

TEACHING SUGGESTIONS

1. The effect of sample size on a confidence interval can be demonstrated with a simple

spreadsheet program such as Excel. Let’s assume that p has been found to be 40 percent,

what would be the confidence intervals under successively larger sample sizes? The

following table is a spreadsheet-like comparison for 95 percent confidence intervals.

Sample Size Lower Limit Upper Limit Range

100 30.4% 49.6% 19.2%

250 33.9% 46.1% 12.1%

500 35.7% 44.3% 8.6%

1000 37.0% 43.0% 6.1%

1500 37.5% 42.5% 5.0%

2000 37.9% 42.1% 4.3%

2. The effect of variability in the sample statistic can be illustrated in the same way.Let’s hold

the sample size at 250, and compare different sizes of p.

Statistic (p) Lower Limit Upper Limit Range

50% 43.8% 56.2% 12.4%

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40% 33.9% 46.1% 12.1%

30% 24.3% 35.7% 11.4%

20% 15.0% 25.0% 9.9%

10% 6.3% 13.7% 7.4%

5% 2.3% 7.7% 5.4%

3. Some textbooks, particularly statistics textbooks, explicitly state the alternative

hypothesis.We do not do so in our textbook, however Instructors who believe students should

understand the concept of an alternative hypothesis may wish to add material of their own on

the concept of an alternative hypothesis.

4. With the XL Data Analyst available to them, students may not appreciate doing hand

calculations of confidence intervals or hypothesis tests. These calculations are more than

tedious exercises. The point is to have students see what is in the numerator and what is in

the denominator of each formula, so they can understand what is driving the computed value.

Typically, the sample size is always in the denominator, while the hypothesized value and

sample statistic are in the numerator. Larger sample sizes drive the computed value (e.g., a

t-value) down; whereas, larger differences between the sample statistic and the hypothesized

value will drive it up.

5. This chapter is the first encounter for students with XL Data Analyst statistical test output

(namely, hypothesis tests).The text describes each interpreted output example in some detail;

however, the statistical values are reported in the output as well.Instructors who prefer to

have their students work with statistical values will find it useful to spend class time on how

to find and interpret the findings.

6. Strictly speaking, the use on any generalization analysis (confidence interval, or hypothesis

test) requires the use of random sampling. However, a true random sample is rare due to

difficulties in acquiring complete population listings and high refusal rates. Instructors who

use student projects or other datasets that are created with the use of convenience sampling or

otherwise nonrandom sampling methods may opt to include a footnote to the effect that the

sample is assumed to be random for educational purposes.

7. Instructors will find Marketing Research Application 12.1, “How to Estimate Market

Potential Using a Survey’s Findings,” a useful demonstration of the economic impact of their

university on specific, local businesses by doing the following:

a. Have students or student teams identify some local establishment patronized by

university students. Examples are: pizza place, coffee shop, restaurant, bar, etc.

b. Using a convenience sample determine the following:

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i. Percent of the sample that patronized the establishment in the past month

ii. Average number of times in the past month the establishment was

patronized by those who used it.

iii. Average amount spent per visit at the establishment

c. The “Best Estimate” of the university student population annual sales is computed

as follows:

i. University student population size times

ii. Percent of sample that patronized the establishment in the past month

times

iii. Average number of times in past month the establishment was patronized

by those who used it times

iv. Average amount spent per visit at the establishment times

v. 12 months

d. “Pessimistic” and “optimistic” sales estimates can be made using the confidence

intervals approach described in the Marketing Research Application.

e. Because a nonrandom sample is used, be sure to use the footnote described in the

above teaching suggestion (#6.).

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