Chapter 7. Hypothesis Testing with One Sample

202 Chapter 7: Hypothesis Testing with One Sample12. Let σ be the population standard deviation of women biologists’ salaries. The claim is that this standarddeviation is greater than 3,000, or σ >3,000. If this is true then σ ≤3,000 must be false. Since σ ≤3,000includes equality, we let H 0 be σ =3,000 and we let H 1 be σ >3,000.In Exercises 13-20,find the critical z values. In each case, assume that the normal distribution applies.13. In a two-tailed test, the critical values are ±z α /2. Since α=0.05, α/2 = 0.025. The critical values are then±z α /2=±z .025=±1.96.14. In a two-tailed test, the critical values are ±z α /2. Since α=0.01, α/2 = 0.005. The critical values are then±z α /2=±z .005=±2.575.15. In a right-tailed test, the critical value is z α. Since α=0.01, the critical value is z α= z .01= 2.33.16. In a left-tailed test, the critical value is −z α. Since α=0.05, the critical value is −z α=−z .01=−1.645.17. Since H 1 is p≠0.17, this is a two-tailed test. In a two-tailed test, the critical values are ±z α /2. Since α=0.10, α/2= 0.05. The critical values are then ±z α /2=±z .05=±1.645.18. Since H 1 is p>0.18, this is a right-tailed test. In a right-tailed test, the critical value is z α. Since α=0.10, thecritical value is z α= z .10= 1.28.19. Since H 1 is p