1. Two Sample Problem
Sometimes we will be interested in comparing means in two
independent populations (e.g. mean income for male and females).
We consider two basic scenarios: populations are normal or
populations are not normal but the sample sizes are large.
In each of these two scenarios we distinguish between few cases…
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2. Case 1 – Variances are known
Two independent populations, both normal variances known.
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3. Case 2 – Variances are known and equal
Two independent populations, both normal variances known and equal.
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4. Case 3 – Variances unknown and equal
Two independent populations, both normal variances equal but
unknown.
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5. Case 4 – Large Samples
Two independent populations, variances are equal but unknown,
large samples.
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6. Case 5 – Large Samples
Two independent populations, variances are unknown, large
samples.
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7. Summary
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8. Examples
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9. Special case: Binomial Proportions
Need large samples for CLT results…
Example:
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10. One Sample Variance
In many case we will be interested in making inference about the population variance.
Suppose X1, X2,…,Xn are random sample from N(μ, σ2) where both
μ and σ are unknown. A CI for σ2 is …
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11. Example
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12. Two Sample Variance
In many case we will be interested in comparing the variances of two independent populations.
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13. Example
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