Question: In (a) – (e) below, you may assume that the data are a simple random sample (or samples) from a normal distribution (or distributions).

a. Consider the setting of a single sample of size n=15. Suppose that the variance is NOT known. Suppose further that it is of interest to construct a 90% confidence interval estimate of the population mean μ. What are the values of the confidence coefficients? Hint: This question is asking you to provide the correct percentiles from the correct distribution.

b. For a single sample size n=35 and the estimation of a variance parameter. σ²

using a 95% confidence interval, what are the values of the confidence coefficients?. Hint: This question is asking you to provide the correct percentiles from the correct distribution.

c. For a single sample size of n=25 and the estimation of the population mean μ when the variance is known using a 80% confidence interval, what are the values of the confidence coefficients? Hint: This question is asking you to provide the correct percentiles from the correct distribution.

d. Next, consider the setting of two independent samples, one with sample size n₁ = 13 and the other with sample size n₂ = 22, and estimation of the difference between the two population means, [ μ ₁- μ ₂ ] . Assume that the two population variances are both unknown and unequal. Suppose further that the two sample variances are S²₁=2.20 and S²₂=0.70. If it is of interest to construct a 95% confidence interval estimate of [ μ ₁- μ ₂ ] , what are the values of the confidence coefficients? Hint: This question is asking you to provide the correct percentiles from the correct distribution.

e. Finally, consider again the setting of two independent samples, one with sample size n₁ = 13 and the other with sample size n₂ = 22. Here, however, it is of interest to construct a 90% confidence interval estimate of the ratio of the two population variances,

[ σ₁²/σ₂² ] . Assume again that the two sample variances are S²₁=2.20 and S²₂=0.70

What are the values of the confidence coefficients? Hint: This question is asking you to provide the correct percentiles from the correct distribution.