Forms for Null and Alternative Hypothesis

Title

• hypothesis tests in chap 12 - Hypothesis Test involve 2 population parameters:
  • population mean
  • population proportion
• for hypothesis tests involving population mean, let ${\mu }_0$: hypothesized value, choose 1 one 3 forms of hypothesis test
  1. $H_0:\mu \ge {\mu }_0,H_a:\mu <{\mu }_0$, lower one-tailed (left tail)
  2. $H_0:\mu \le {\mu }_0,H_a:\mu >{\mu }_0$, upper one-tailed (right tail)
  3. $H_0:\mu ={\mu }_0,H_a:\mu \ne {\mu }_0$, two-tailed
• following the Test claim using a confidence interval (a, b), the below is the conclusion for each case:
  • Reject $H_0$: there is enough evidence to conclude $H_a$
  • Can/Do not reject $H_0$: do not have enough evidence to conclude $H_a$