# statistics

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A random sample of n = 30 is drawn from a population that is normally distributed, and the sample variance is s©÷ = 41.5. Use ¥á = 0.05 in testing ¥Ç₀ : ¥ò©÷ = 29.0 versus ¥Ç©û : ¥ò©÷ ¡Á 29.0

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The following is a reproduction of the post in Western encoding:
"A random sample of n = 30 is drawn from a population that is normally distributed, and the sample variance is s² = 41.5. Use α = 0.05 in testing Η₀ : σ² = 29.0 versus Η₁ : σ² ≠ 29.0"

s²/σ² = 41.5/29 = 1.431

The Chi-squared statistic for α = 0.95 and df=30-1=29 is 42.6.

Thus 95% of the samples of size N=30 would be such that
s²/σ² < 42.6/29=1.469

Since 1.431 < 1.469, we conclude that
Η₀ : σ² = 29.0 is accepted for α = 0.05.

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Thank you MathMate

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You're welcome.

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