Lesson 9: Hypothesis Testing

• Levels of likelihood
  • Probabilities statisticians have determined to be "likely" or "unlikely"
  • Alpha levels (very unlikely):
    • .05 (5%) (z-score = 1.64)
    • .01 (1%) (z-score = 2.33)
    • .001 (0.1%) (z-score = 3.1)

• Critical Regions

  • If probability is less than alpha level, will fall in the critical region in distribution:

  

  • If we got a sample mean at 1.95, you might say "mean is significant at p < .05"
  • Above 2.33? "significant at p < .01"
  • Two-tail critical values
  • When you need to consider both ends of the distribution
  • .05% needs to be divided in half: 2.5% * 2

  

  • Alpha levels (for two-tailed tests):
    • 0.05 - 1.65
    • 0.01 - 2.32
    • 0.001 - 3.08
  • Null hypothesis vs alternative hypothesis
  • With a sample: can't prove null hypothesis is true, can only get evidence to reject it or fail to reject it

  * Rejecting the null * sample mean falls within the critical region * z-score of sample mean is greater than z-critical value * probability of obtainig the sample mean is less than the alpha level * Decision errors * Type 1 error: reject the null and it's true * Type 2 error: retain the null and it's false