### Estimating and testing population variance

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Estimating and testing population variance

A simple random sample was drawn from a normal population with unknown variance σ²: Observation: 1, 2, 3, 4, 5 x: 13.9, 18.8, 19.2, 15.6, 21.5

a. What information justifies a Chi-square sampling distribution of (n-1)s²/σ²?

b. Use Excel to complete the lookup table below.

c. Construct the 97.5% confidence interval for σ².

d. At the level of significance α = 0.025, test H0: σ² = 8.4 versus H1: σ² ≠ 8.4. Find p-value.

e. At the level of significance α = 0.10, test H0: σ² ≤ 8.9 versus H1: σ² > 8.9. Find p-value.

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