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Two Sample Tests of Hypothesis and
Analysis of Variance in Excel
Dr. Rick Jerz
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Four Scenarios
• Two independent samples1. Population standard deviations are known and
equal2. Population standard deviations are not known,
but equal3. Population standard deviations are not known,
and not equal• Two dependent samples
4. There is no difference
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Format of Hypotheses
• The hypotheses for comparing two independent population means, μ1 and μ2, are:
• The hypothesis for comparing two dependent population means, μ1 and μ2, is:
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Possible Independent Samples Scenarios
1. Population σ 2’s are known2. Population σ 2’s are unknown
1. Are σ 2’s equal?2. Are σ 2’s unequal?
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Comparing Two Variances –F Statistic
• Format of hypotheses• To test whether two population means are
equal, we may also need to test whether two population variances are equal.
• The hypotheses may be stated as
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“Special” Test Statistics
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Alternative Excel Method – Data Analysis Add-in
• Excel: Data|Data Analysis
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Excel Model Overview
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Population Variances Known
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Population Variances Known
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Population Variances Unknown
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Population Variances Unknown
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Population Variances Unknown
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Population VarianceUnknown and Unequal
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Solution: Population VariancesUnknown and Unequal
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Population VariancesUnknown and Unequal
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Solution: Population VariancesUnknown and Unequal
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Residential Home Appraisal Paired-Samples Example
• Nickel Savings and Loan wishes to compare the two companies it uses to appraise the value of residential homes. Nickel Savings selected a sample of 10 residential properties and scheduled both firms for an appraisal. The results, reported in $000, are:
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Residential Home Appraisal Example
• At the .05 significance level, can we conclude there is a difference between the firms’ mean appraised home values?
• Solving this by hand?
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Residential Home Appraisal Example
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Residential Home Appraisal Example
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