Basic Computation: Confidence Interval for m1 2m2 Consider two independent normal distributions. A random sample of size n1 5 20 from the first distribution showed x1 512 and a random sample of size n2 5 25 from the second distribution showed x2 514.

(a) Check Requirements If s1 and s2 are known, what distribution does x1 2x2 follow? Explain.

(b) Given s1 5 3 and s2 5 4, find a 90% confidence interval for m1 2m2.

(c) Check Requirements Suppose s1 and s2 are both unknown, but from the random samples, you know s1 5 3 and s2 5 4. What distribution approximates the x1 2x2 distribution? What are the degrees of freedom? Explain.

(d) With s1 5 3 and s2 5 4, find a 90% confidence interval for m1 2m2.

(e) If you have an appropriate calculator or computer software, find a 90% confidence interval for m1 2m2 using degrees of freedom based on Satterthwaite’s approximation.

(f) Interpretation Based on the confidence intervals you computed, can you be 90% confident that m1 is smaller than m2? Explain.

AppendixLO1