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

(a) 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.

(b) 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 H₁: µ ≠ 0 at \[\alpha \] = 0.05?

(c) 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.

(d) 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?

(e) Given the following information, calculate s_p², the pooled sample variance that should be used in the pooled-variance t test.

s₁² = 9 s₂² = 4

n₁ = 26 n₂ = 16