chapter 12 assignment

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Basic Marketing Research: Using Microsoft Excel Data Analysis, 3rd edition

Alvin C. Burns Louisiana State University Ronald F. Bush University of West Florida

Generalizing a Sample’s Findings

• We refer to a ____________ whenever a percent or average or some other analysis value is computed with a sample’s data.

• If we are measuring only a subset of the population

• However, because of the sample error involved, the sample finding must be considered an approximation of the ___________,

• If we measured EVERY PERSON in the population

• Sample Findings will ALWAYS have some ______ in estimating the Population Fact

Generalizing a Sample’s Findings, Continued...

• Generalization is the act of estimating a population fact from a sample finding.

• Generalization is a form of logic in which you make an inference about an entire group based on some evidence about that group.

• There are just two types of evidence:

• The variability (_____ is more evidence/good)

• The sample size (______ is more evidence/good)

Generalizing a Sample’s Findings, Continued...

There is MORE variability (a wider estimation) when we have LESS observations in

the sample!

See how much MORE PRECISE (less variable) the

larger sample is at estimating the population!

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Estimating the Population Value

• Population parameters are designated by _______letters such as π (percent) or µ (mean or average)

• Sample findings are relegated to lowercase _______letters such as p (percent) or (average or mean).

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How to Estimate a Population Percentage (Categorical Data)

• A confidence interval is a _______ (lower and upper boundary) into which the researcher believes the population parameter falls with an associated degree of confidence (typically 95% or 99%).

How to Estimate the Population Value for a Percentage

How to Estimate the Population Value for a Percentage, Continued...

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Calculation of Confidence Intervals

95% Confidence Interval 99%Confidence Interval

The Variability Affects the Sampling Distribution

How Variability Affects the 95% Confidence Interval for a Percentage

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

• The menu sequence to direct the XL Data Analyst to compute a confidence interval for a percentage is Generalize-Confidence Interval-Percentage …

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

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How to Estimate a Population Average (Metric Data)

How to Estimate the Population Value for an Average

How to Estimate the Population Value for an Average, Continued...

Calculation of a 99% Confidence Interval for an Average

You can be 99% confident that the population average falls in the range of 39.8 to 50.2 minutes.

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Obtaining a 95% Confidence Interval for an Average with XL Data Analyst

• Generalize-Confidence Interval-Average

Obtaining a 95% Confidence Interval for an Average with XL Data Analyst, Continued...

Testing Hypotheses About Percents or Averages

• Someone makes a prediction about the population value based on prior knowledge, assumptions, or intuition. This statement, called a __________ , commonly takes the form of an exact specification of the population parameter.

• In other words, you are making a “guess” about an average OR a percent (or a difference between groups, etc) BEFORE you do the analysis

Testing a Hypothesis About a Percentage

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How to Test a Hypothesis for a Percentage How to Test a Hypothesis for a Percentage, Continued...

The Logic of Hypothesis Testing

• Recall that we assumed our hypothesis is correct! If that is true we would expect our sample’s z score to fall within +/- 1.96z. If it does, then that is strong evidence to support our hypothesis.

• If our hypothesis is correct, there is only a 5% chance we will get a z score that falls outside of +/- 1.96z.

The Logic of Hypothesis Testing, Continued...

If the z value falls in the acceptance region, there is support for the hypothesis, and if the z value falls in the rejection region, there is no support for the hypothesis.

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Example of a Hypothesis Test

• What percent of U.S. college students own a major credit card?

• Let’s say that you think three of every four college students (75%) own a Mastercard, Visa, or some other major credit card.

• A recent survey of 1,200 students on U.S. college campuses found that 84% have a major credit card.

Example of a Hypothesis Test, Continued...

• Compute the z value & see if it falls within the acceptance region or not

Answer: z = - 8.2

If the hypothesis were true, there is a 95% chance that the computed z would be within ±1.96. Since it is -8.2, we ______ the hypothesis!

Testing a Directional Hypothesis

• A directional hypothesis is one that indicates the direction in which you believe the population parameter falls relative to some hypothesized average or percentage.

• If you are testing a directional (“greater than” or “less than”) hypothesis, the critical z value is adjusted downward to 1.64 and 2.33 for the 95% and 99% levels of confidence, respectively.

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

• The menu sequence to direct XL Data Analyst to accomplish this is Generalize-Hypothesis Test-Percentage…

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How to Test a Hypothesis About a Percentage with XL Data Analyst, Continued...

If you inspect the statistical values in XL Data Analyst output, there is reference to a “t” value and no reference to a “z” value.

You should treat the “t” values as the equivalent to the “z” values.

Testing a Hypothesis About an Average

Testing a Hypothesis About an Average, Continued...

$3,750 $3,800

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

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

If the hypothesis is true, then 95% of the sample results will fall between +/- 1.96 standard errors of the hypothesized mean.

If the hypothesis is incorrect, there is a strong likelihood that the sample findings will fall outside of +/- 1.96 standard errors.