Let X be N(, 100). To test H0: = 80 against H1: > 80, let the critical region be defined by C = {(x1, x2, ... , x25) : x 83}, where x is the sample mean of a random sample of size n = 25 from this distribution. (a) What is the power function K() for this test? (b) What is the significance level of the test? (c) What are the values of K(80), K(83), and K(86)? (d) Sketch the graph of the power function. (e) What is the p-value corresponding to x = 83.41?

STAT-5615: Statistics in Research I Lecture 6 Con▯dence Intervals Ott & Longnecker 4.12, 5.2, 5.3, 5.7 Dr. Christian Lucero Virginia Tech Fall 2016 Topics for this Lecture 1. The General Idea Behind Interval Estimation. 2. Student’s t Distribution 3. Con▯dence Intervals for a single mean m when s is known. 4. Con▯dence Intervals for a single mean m when s is unknown. 5. Interpretation of the Con▯dence Interval. 6. Factors that control the width of CIs. Review 1. Sample Variation and Point Estimation 2. Probability and Probability Distributions 3. Random Variables I Understand the di▯erence between the notati