Question: Write a short answer to each of the following:

1. What are the properties of Student’s t distribution? How does it differ from the Normal distribution? Give an example where using t distribution is more appropriate than using a Normal distribution.
2. A 95% confidence interval for \[\mu \] is from -20 to 25. What conclusion can we make based on this confidence interval if we test H _o : µ = 0 against H ₁ : µ ≠ 0 at \[\alpha \] = 0.05?
3. A statistician wishes to determine whether there is evidence that average home price in a posh neighborhood is more than $300,000. State the null and alternative hypotheses for this situation.
4. The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. She performs a two-tailed test of the null hypothesis that the mean for the stressed oak furniture is 650. What are Type I and Type II errors for this problem?
5. Given the following information, calculate s _p ² , the pooled sample variance that should be used in the pooled-variance t test.

s ₁ ² = 9 s ₂ ² = 4

n ₁ = 26 n ₂ = 16

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