ap statisticsFRAPPY! chapter 12inference for proportions

ideal solution part aParameter: p is the proportion of all

the specified make and model that have the defect.

HO: p = 0.05 (the proportion of this make and model with the defect is 5%)

HA: p > 0.05 (the proportion of this make and model with the defect is greater than 5%)

scoring part aEssentially correct (E) if the student

1) correctly defines the parameter of interest

2) gives correct null and alternative hypotheses

Partially correct (P) if only one of the two elements above is present.

ideal solution part b – section 1

DefinitionType I error: the law firm believes that

the proportion of cars that have the defect is greater than 0.05, when in fact it is not.

Type II error: the law firm is not convinced that the proportion of cars that have the defect is greater than 0.05, when in fact it is.

scoring part b – section 1Essentially correct (E): if

1) the student correctly defines Type I and Type II errors for the stated hypotheses in part a

2) the definition of the two types of errors is in the context of the problem and consistent with the hypotheses given in part a

scoring part b – section 1… cont’d

Partially correct (P)• The definitions of the errors are

correct but not in context• The definitions are in context, but

Type I and Type II are reversed• The definition of only one error is

given correctly and in context

ideal solution part b – section 2

ConsequenceType I error: the firm will not cove its

expenses, resulting a loss to the firmType error: the firm will miss an

opportunity to make money on this case

scoring part b – section 2Essentially correct (E) if

1) it discusses the consequences of each type of error

2) the discussion of consequences is consistent with the definition of

Type I and Type II errors given in part b section 2

…scoring part b – section 2Partially correct (P) if• The consequences of only one type of

error are discussed correctly• The student identifies consequences of

two types of error, but the consequences are associated with the wrong type of error

• The student correctly identifies for both errors that they take the case or that they do not take the case, but does not give economic consequences

score time!

4 (complete response) EEE3 (substantial response) EEP2 (developing response) EEI EPP

PPP1 (minimal response) EPI EII

PPI

*Note – order is not important for scoring!

reflection timeTake a moment to discuss with your

partner(s) any strengths or weaknesses you observed while completing this FRAPPY. What would you have changed? What were you the most confident about? Does anyone have anything they would like to share?