ࡱ> ;=89: 0<bjbjBrBr   ;1<<!!!!!4'"'"'"h"##'"&$5$$$$e.>.. @!.C."e...!!$$h Ԇ222.!R$!$2.22.d!"$аBN'"0dwF06#1J!=l2...2................< E :  Internal Assessment Resource Mathematics and Statistics Level 3 This resource supports assessment against: Achievement Standard 91582 Use statistical methods to make a formal inferenceResource title: New Zealand crash statistics4 creditsThis resource: Clarifies the requirements of the standard Supports good assessment practice Should be subjected to the schools usual assessment quality assurance process Should be modified to make the context relevant to students in their school environment and ensure that submitted evidence is authentic Date version published by Ministry of EducationDecember 2012 To support internal assessment from 2013Quality assurance statusThese materials have been quality assured by NZQA. NZQA Approved number A-A-12-2012-91582-01-6188Authenticity of evidenceTeachers must manage authenticity for any assessment from a public source, because students may have access to the assessment schedule or student exemplar material. Using this assessment resource without modification may mean that students work is not authentic. The teacher may need to change figures, measurements or data sources or set a different context or topic to be investigated or a different text to read or perform. Internal Assessment Resource Achievement Standard Mathematics and Statistics 91582: Use statistical methods to make a formal inference Resource reference: Mathematics and Statistics 3.10B Resource title: New Zealand crash statistics Credits: 4 Teacher guidelines The following guidelines are supplied to enable teachers to carry out valid and consistent assessment using this internal assessment resource. Teachers need to be very familiar with the outcome being assessed by Achievement Standard Mathematics and Statistics 91582. The achievement criteria and the explanatory notes contain information, definitions, and requirements that are crucial when interpreting the standard and assessing students against it. Context/setting This activity requires students to carry out an investigation that uses statistical methods to make a formal inference about New Zealand crash statistics. This activity has been motivated by recent successful media campaigns by the New Zealand Transport Association (for example, see this website  HYPERLINK "http://www.nzta.govt.nz/about/advertising/drink-driving/legend.html" http://www.nzta.govt.nz/about/advertising/drink-driving/legend.html). It would be appropriate to share one or two of these advertisements with the students to introduce them to the context. Before the assessment, students need to research the context, including details about the variables. Time needs to be set aside for this purpose before the assessment. This activity can be adapted to use another existing data set. Any data set provided needs to have appropriate motivation, contextual depth, and relevance to the students. Details about the data collection methods need to be provided to enable students to inform themselves about the context and populations. Conditions This activity requires multiple sessions to complete an investigation. Confirm the timeframe with your students. Students will present their work and findings independently. The students are expected to use appropriate technology, for example, statistical software. Resource requirements This data set should be made available as a spreadsheet for students to use for the assessment. The descriptions of the variables can be found in Resource A. Additional information None. Internal Assessment Resource Achievement Standard Mathematics and Statistics 91582: Use statistical methods to make a formal inference Resource reference: Mathematics and Statistics 3.10A Resource title: New Zealand crash statistics Credits: 4 AchievementAchievement with MeritAchievement with ExcellenceUse statistical methods to make a formal inference.Use statistical methods to make a formal inference, with justification.Use statistical methods to make a formal inference, with statistical insight.Student instructions Introduction Following on from the successful Legend media campaign, the Ministry of Transport commissioned a study of drivers from the age groups that have the highest risk of crashing and the lowest risk of crashing. This assessment activity requires you to produce a report describing an investigation that uses statistical methods to make a formal inference related to New Zealand crash statistics. You will work independently over a period of <> to pose a comparison investigative question, complete an analysis, make conclusions, and write your report. The quality of thinking demonstrated in your report and your ability to link the context and populations to the different components of the statistical enquiry cycle will determine your overall grade. Task In 2011, there were 1409 serious or minor crashes where alcohol or drugs were recorded as a factor. A random sample was taken from these drivers and they were interviewed in person by researchers. You have been provided with a data set from the random sample of drivers (see Resource A for variable definitions). Use the statistical enquiry cycle to conduct your investigation and write a report describing the investigation. Familiarise yourself with the data set provided. This will include doing research to help you understand the variables and develop a purpose for the investigation. Identify the variables you wish to investigate, and establish a related investigative comparison question. Conduct your investigation and write a report containing: your comparison investigative question appropriate displays and summary statistics a discussion of the sample distributions an appropriate formal statistical inference a conclusion communicating your findings, which may include discussing sampling variability, including the variability of estimates and reflecting on the process that has been used to make the formal inference. As you write your report, take care to link your discussion to the context and to support your statements by referring to statistical evidence. Resource A: Variable definitions in the data set VariableDescriptionGenderMale FemaleAgeAge in years at time of crashRisk groupHighest risk age group 15-24 years (H) Lowest risk age group 50-59 years (L)Licence typeType of licence held at time of crash Learners (L) Restricted (R) Full (F)Crash severityMinor injury crash (M) Serious injury crash (S)Blood alcohol levelRecorded blood alcohol level recorded at time of crash (in milligrams of alcohol per 100 millilitres of blood breath test results have been converted to a blood equivalent)Distance drivenEstimated distance driven in the last week (in kilometres) Distance from homeEstimated distance away from home when crash occurred (in kilometres)Vehicle ageAge of vehicle involved in crashInsurance payoutValue of insurance claimMedical expensesEstimated medical costs as a result of the crash (total costs to date)Time off workEstimated number of days off work as a result of the crash (if applicable) Assessment schedule Mathematics and Statistics 91582 New Zealand crash statistics Teacher note: You will need to adapt this assessment schedule to include examples of the types of responses that can be expected. Evidence/Judgements for Achievement Evidence/Judgements for Achievement with MeritEvidence/Judgements for Achievement with ExcellenceThe student has used statistical methods to make a formal inference. The student has: produced a report that shows they have used each component of the statistical enquiry cycle to make a formal inference posed a comparison investigative question using a given multivariate data set selected and used appropriate displays and summary statistics discussed sample distributions discussed sampling variability, including variability of estimates made an appropriate formal statistical inference communicated findings in a conclusion For example: Problem The question is a comparison investigative question that clearly identifies the comparison and the population(s). Analysis Dot plots and box and whisker plots are produced and summary statistics, including the difference between the sample medians, have been calculated. The sample distributions are discussed and compared in context. This could involve comparing the shift/centre, spread, shape, and unusual features using features of the displays and the summary statistics. A formal statistical inference is made by using resampling (bootstrapping) to construct a confidence interval. Conclusion The formal inference is used to answer the investigative question. An understanding of sampling variability is evident. The examples above are indicative of the evidence that is required. The student uses statistical methods to make a formal inference, with justification. The student has: produced a report that gives evidence of linking components of the statistical enquiry cycle to the context and/or populations, and referring to evidence such as sample statistics, data values, or features of visual displays in support of statements made posed a comparison investigative question using a given multivariate data set selected and used appropriate displays and summary statistics discussed sample distributions discussed sampling variability, including variability of estimates made an appropriate formal statistical inference communicated findings in a conclusion For example: Problem A comparison investigative question has been posed and includes an explanation for the choice of variables for the investigation. Analysis Dot plots and box and whisker plots are produced and summary statistics, including the difference between the sample medians, have been calculated. The sample distributions are discussed and compared in context. This will involve comparing the shift/centre, spread, shape, and unusual features with reference to features of the displays and the summary statistics and links to the population or investigative question. A formal statistical inference is made by using resampling (bootstrapping) to construct a confidence interval. Conclusion The formal inference is used to answer the investigative question, justifying the call and making links to the context. The conclusion includes an interpretation of the confidence interval. An understanding of sampling variability is evident. The examples above are indicative of the evidence that is required.The student uses statistical methods to make a formal inference, with statistical insight. The student has: produced a report that gives evidence of integrating statistical and contextual knowledge throughout the statistical enquiry cycle, and may include reflecting about the process and considering other relevant explanations posed a comparison investigative question using a given multivariate data set selected and used appropriate displays and summary statistics discussed sample distributions discussed sampling variability, including variability of estimates made an appropriate formal statistical inference communicated findings in a conclusion For example: Problem The research is used to develop the purpose for their investigation and the contextual knowledge is used to pose a comparison investigative question. Analysis Dot plots and box and whisker plots are produced and summary statistics, including the difference between the sample medians, have been calculated. The sample distributions are discussed and compared in context. This includes seeking explanations for features of the data identified and considering the impact of these on the context or investigative question. A formal statistical inference is made by using resampling (bootstrapping) to construct a confidence interval. Conclusion The formal inference is used to answer the investigative question, justifying the call and linking back to the purpose of the investigation. The conclusion includes an interpretation of the confidence interval. Findings are clearly communicated and linked to the context and populations. There is a reflection that the process (which may include discussing sampling variability) or other explanations for the findings have been considered which may involve re-examining the data from a different perspective. The examples above are indicative of the evidence that is required.Final grades will be decided using professional judgement based on a holistic examination of the evidence provided against the criteria in the Achievement Standard.     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