In reality decision null hypothesis is true null

  • DeAnza College
  • MATH 10
  • Notes
  • HamsterNation
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IN REALITY: DECISION: Null Hypothesis is TRUE Null Hypothesis is FALSE Alternate Hypothesis is true Based on sample data we DECIDE NOT TO REJECT null hypothesis (Data favors null hyothesis) Correct Decision Type II Error: Wrong Decision Probability is β Based on sample data we DECIDE TO REJECT null hypothesis (Data favors alternate hyothesis) Type I Error: Wrong Decision Acceptable probability (risk) is α α is called significance level Correct Decision Probability is 1 − β 1 − β is called the power Type I Error: Rejecting the null hypothesis when in reality the null hypothesis is true concluding (based on sample data) in favor of the alternate hypothesis when in reality the null hypothesis is true The probability you are willing to risk of making a Type I error is denoted by α (Greek letter alpha). α is called the (pre-determined) significance level of the hypothesis test . The significance level α should be small: a low risk of incorrectly rejecting the null hypothesis if it is really true Type II Error: Failing to reject the null hypothesis when in reality the null hypothesis is false concluding (based on sample data) in favor of the null hypothesis when in reality the alternate hypothesis is true The probability of Type II error is denoted by β (Greek letter beta). 1 − β is called the power of the hypothesis test. The power of a hypothesis test should be large: large probability of correctly rejecting a false null hypothesis A Court Trial is a real-life example of a hypothesis test: Null Hypothesis: Not Guilty: A person is assumed to be innocent Alternate Hypothesis: Guilty: A person must be proven guilty beyond a reasonable doubt IN REALITY: DECISION: Null Hypothesis is TRUE Person is NOT GUILTY Null Hypothesis is FALSE Person is GUILTY Based on evidence presented in court jury decides NOT GUILTY Correct Decision Wrong Decision Type II Error Based on evidence presented in court jury decides GUILTY Wrong Decision Type I Error Correct Decision
Example A: (see page 1 for the statement of this problem) p = true population proportion of all people with this knee injury who would be cured if they had this knee surgery Ho: p . 60 Ha: p > A Type I error would be to conclude that this surgery cures more than 60% of all knee injuries of this type, when in reality it cures 60% or fewer of all such injuries. . 60
Page 4 Some of the examples on page 2 will be used in class to interpret errors; Catalyst website has a link to all answers. Example #____: A Type I Error is concluding that_________________________________________________________ when in reality_______________________________________________________________________ A Type II Error is concluding that________________________________________________________ when in reality_______________________________________________________________________ Example #____: A Type I Error is concluding that_________________________________________________________ when in reality_______________________________________________________________________ A Type II Error is concluding that________________________________________________________ when in reality_______________________________________________________________________ Example #____: A Type I Error is concluding that_________________________________________________________ when in reality_______________________________________________________________________ A Type II Error is concluding that________________________________________________________ when in reality_______________________________________________________________________ Example #____: A Type I Error is concluding that_________________________________________________________ when in reality_______________________________________________________________________ A Type II Error is concluding that________________________________________________________

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