PROBLEM 9E

Let p denote the probability that, for a particular tennis player, the first serve is good. Since p = 0.40, this player decided to take lessons in order to increase p. When the lessons are completed, the hypothesis H0: p = 0.40 will be tested against H1: p > 0.40 on the basis of n = 25 trials. Let y equal the number of first serves that are good, and let the critical region be defined by C = {y: y ≥ 14}.

(a) Find the power function K(p) for this test.

(b) What is the value of the significance level, α =K(0.40)? Use Table II in Appendix B.

(c) Evaluate K(p) at p = 0.45, 0.50, 0.60, 0.70, 0.80, and 0.90. Use Table II.

(d) Sketch the graph of the power function.

(e) If y = 15 following the lessons, would H0 be rejected?

(f) What is the p-value associated with y = 15?

References Table II in Appendix B

PSYCH STATS POWERPOINT CHAPTER TWO ● frequency: the number of times a score occurs ● distribution: shape of scores ● frequency distribution: organized display of scores ○ descriptive stats ● tables: simplest format ○ lists every score and frequency ● graphs ○ visual depiction ○ many types Frequency Distribution Table ● find the largest value, write it in the table ● find each time it occurs, record frequency ● repeat ● sum of all scores ○ take each individual score from table ○ multiply each score by the frequency ● proportion: f/n ● percentage: (f/n)100 ● the sum of all the total number of frequencies: n ● if your data set has a large range: use a group frequency table