12 - Hypothesis Test

Title

• Null hypothesis:
  • $H_0$: tentative assumption about a population parameter, an assumption to be challenged
• Alternative hypothesis
  • $H_a$: opposite to null hypothesis, a currently testing hypothesis
• Forms for Null and Alternative Hypothesis
• Type 1 and Type 2 errors & Consequence
• Level of Significance
• Population mean, std known
• Population mean, std unknown
• Population proportion
  • use proportion calculation using z-test
  • $p_0$: hypothesized value for the population proportion
  • 3 forms of hypothesis test:
    • $H_0:p\ge p_0,H_a:p<p_0$
    • $H_0:p\le p_0,H_a:p>p_0$
    • $H_0:p=p_0,H_a:p\ne p_0$
  • Hypothesis test based on the difference btw $\bar{p}$ and $p_0$
  • test statistic: $ts=\frac{\bar{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$
  • p-value calculation