ࡱ> ~ kDbjbj vcc9&&'''D'''](l('3P2e)L)X * **_4u7Y8tOOOOOOO$eSV&O'8g3"388O&& **H O===8&8 *I'8*O=8O==:JD1''ZL*./}s9~K&OP03PKAW=:AWDZLZLAW'nL088=88888OO=8883P8888AW888888888 %:  Internal Assessment Resource Mathematics and Statistics Level 2 This resource supports assessment against: Achievement Standard 91264 version 3 Use statistical methods to make an inferenceResource title: SURFing4 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 EducationFebruary 2017 Version 4 To support internal assessment from 2017Quality assurance statusThese materials have been quality assured by NZQA. NZQA Approved number: A-A-02-2017-91264-04-5789Authenticity 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 91264: Use statistical methods to make an inference Resource reference: Mathematics and Statistics 2.9A v4 Resource title: SURFing Credits: 4 Teacher guidelines The following guidelines are designed to ensure that teachers can 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 91264. 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 assessment activity requires students to pose a comparative question based on the Household Savings SURF dataset from Statistics New Zealand, investigate the question, and present a report of their results. The Household Savings SURF for Schools is a synthetic unit-record file (SURF) containing 300 records and eleven variables based on data from the 2001 Household Savings Survey (HSS), and is located at:  HYPERLINK "http://www.stats.govt.nz/methods_and_services/schools_corner/SURF%20for%20schools.aspx" http://www.stats.govt.nz/methods_and_services/schools_corner/SURF%20for%20schools.aspx. This activity can be adapted to use the New Zealand Income Survey SURF, or a similar electronic database. Conditions This assessment activity requires multiple sessions. Confirm the timeframe with your students. Students must work independently. Students may use suitable technology, including statistical software for graphing and preparation of summary statistics. Ensure the students have relevant background information about the SURF data set. The format of the presentation could be, but is not restricted to, a computer slideshow, a written report, or an oral presentation. Resource requirements Provide students with copies of the Level 2 Mathematics and Statistics formulae sheet. Provide students with access to the SURF Household savings database, either directly via the Internet or by distributing copies of the data file located at:  HYPERLINK "http://www.stats.govt.nz/tools_and_services/services/schools_corner/surf for schools/household-savings-survey.aspx" http://www.stats.govt.nz/tools_and_services/services/schools_corner/surf for schools/household-savings-survey.aspx. Additional information A household savings survey SURF fathom file is available at:  HYPERLINK "http://www.stats.govt.nz/tools_and_services/services/schools_corner/surf%20for%20schools.aspx" http://www.stats.govt.nz/tools_and_services/services/schools_corner/surf%20for%20schools.aspx. Internal Assessment Resource Achievement Standard Mathematics and Statistics 91264: Use statistical methods to make an inference Resource reference: Mathematics and Statistics 2.9A v4 Resource title: SURFing Credits: 4 AchievementAchievement with MeritAchievement with ExcellenceUse statistical methods to make an inference.Use statistical methods to make an inference, with justification.Use statistical methods to make an inference, with statistical insight.Student instructions Introduction Statistics New Zealand collects data about New Zealand and makes it available for research. This assessment activity requires you to review Statistics New Zealand's Household Savings Survey SURF (Synthetic Unit-Record File) dataset, pose a comparative question on a topic of personal interest that can be answered using the dataset, investigate the question, and present a report of your findings. Task The Household Savings SURF for Schools is a synthetic unit-record file (SURF) containing 300 records and eleven variables based on data from the 2001 Household Savings Survey (HSS), located at:  HYPERLINK "http://www.stats.govt.nz/methods_and_services/schools_corner/SURF%20for%20schools.aspx" http://www.stats.govt.nz/methods_and_services/schools_corner/SURF%20for%20schools.aspx. Working independently, carry out a comparative statistical investigation using the Household Savings Survey SURF and prepare a report. Statistical investigation process: Pose an appropriate comparative investigative question that can be answered using the data provided in the Household Savings Survey SURF data set. Select random samples to use to answer your investigative question. You need to consider your sampling method and your sample size. Select and use appropriate displays and measures. Discuss sample distributions by comparing features of them. Discuss sampling variability, including the variability of estimates. Make an inference. Conclude your investigation by answering the investigative question. Report structure: Introduction: The comparative investigative question and purpose of the investigation. Method used to select samples and collect data. Results from your data including analysis. Discussion of your findings. The quality of your discussion and reasoning and how well you link the context to different stages of the statistical enquiry cycle will determine the overall grade. Assessment schedule: Mathematics and Statistics 91264 SURFing Teachers 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 shows evidence of using each component of the statistical enquiry cycle to make an inference. The student has: specified the purpose of the investigation or has a clear investigative question selected random samples with evidence of how this selection was made. The selection is sufficient and relevant to the investigative question selected and used appropriate displays and measures discussed the sample distributions discussed sampling variability, including variability of estimates made a correct inference communicated findings clearly. For example: Problem The question identifies the population, the groups, the variable together with relevant units and is a comparative question about the population medians. Plan and data An appropriate random sample from each group has been generated and the corresponding population data collected. The sampling method is named and sample size stated. Analysis Summary statistics have been calculated (or implied by the box plot) for each group and there is a dot plot and box and whisker graph for each set of sample data. The informal confidence intervals for the population medians have been found (or implied by being shown on the box plot). The distributions are discussed in context - at least two comparative features of the sample distributions (shape, overlap, shift, spread, middle 50%, unusual or interesting features) have been identified. Conclusion The conclusion includes an answer to the investigative question that is consistent with the analysis and references the population. (The answer to the investigative question may be part of the inference.) Sampling variability has been discussed - the fact that different samples will give different intervals or estimates of population parameters has been indicated. An inference (may be part of the analysis) is made using the informal confidence intervals, for example the student has stated they are pretty sure a population median will lie within a correctly calculated interval.The student will make an inference, showing evidence of linking each component of the statistical enquiry cycle to the context, and/or populations and referring to evidence in support of statements made. The student has: specified the purpose of the investigation or has a clear investigative question. The purpose or question link to the situation being investigated selected random samples. The selection is sufficient and relevant to the investigative question. Reference to decisions about method or sample size is made selected and used appropriate displays and measures discussed the sample distributions, using supporting evidence that is linked to the context discussed sampling variability, including variability of estimates made a correct supported inference communicated findings clearly, and has linked findings to the context and populations. For example: Problem . The question identifies the population, the groups, the variable together with relevant units and is a comparative question about the population medians. Plan and data An appropriate random sample from each group has been generated and the corresponding population data collected. Contextual reasons have been given for deciding on the use of a simple random sample or the sample size. Analysis Summary statistics have been calculated (or implied by the box plot) for each group and there is a dot plot and box and whisker graph for each set of sample data. The informal confidence intervals for the population medians have been calculated and plotted. The distributions are discussed in context - At least two comparative features of the sample distributions have been identified and comments have been linked to the investigative question and the population. An inference is made using the informal confidence intervals, for example the student has stated they are pretty sure the population medians will lie within a correctly calculated interval. Conclusion A conclusion about the population medians has been made and justified using the informal confidence intervals. Justification comments are in context and include an interpretation of the informal confidence intervals. There is an answer to the investigative question with contextual comments that are supported by references to specific evidence from the analysis, for example, overlap of intervals. (The answer to the investigative question may be part of the inference.) Sampling variability has been discussed - the fact that different samples will give different intervals or estimates of population parameters has been indicated. Comments, in context, related to the interval have been made, for example, that such an interval would contain the population median in most cases. An understanding of the difference between the sample calculations and population estimates has been demonstrated.The student will make an inference, showing evidence of integrating statistical and contextual knowledge throughout the statistical enquiry cycle. They may reflect on the process or consider other explanations. The student has: specified the purpose of the investigation and the investigative question, and these are relevant to the situation being investigated selected random samples. The selection is sufficient and relevant to the investigative question. Reference to decisions about method and sample size is made selected and used appropriate displays and measures discussed the sample distributions, integrating statistical and contextual knowledge discussed sampling variability, including variability of estimates made a correct supported inference communicated findings clearly and has linked findings to the context and populations. They have justified their inference, integrating contextual and statistical knowledge, or they have reflected about the process, or they have considered other explanations. For example: Problem The question identifies the population, the groups, the variable together with relevant units and is a comparative question about the population medians.There is contextual reflection or explanations relating to aspects of the question. Plan and data An appropriate random sample from each group has been generated and the corresponding population data collected. Contextual reasons have been given for deciding on the use of a simple random sample and the sample size. Analysis Summary statistics have been calculated (or implied by the box plot) for each group and there is a dot plot and box and whisker graph for each set of sample data. Informal confidence intervals for the population medians have been calculated and plotted. The distributions are discussed in context - at least three comparative features of the sample distributions have been identified and contextual knowledge has been used to link comments to the investigative question and the population. Conclusion A conclusion about the population medians has been made and justified using the informal confidence intervals. There is an answer to the investigative question with contextual comments that are supported by references to specific evidence from the analysis, for example, overlap of intervals. An understanding of the difference between the sample calculations and population estimates is demonstrated. The student has reflected on the process or has given explanations by considering, in context, the effect of aspects such as sample size on the estimate. They have discussed aspects of the investigation in context, such as a limiting factor in the definition of the groups, and have identified their impact on the reliability of estimates. Sampling variability has been discussed - the fact that different samples will give different intervals or estimates of population parameters has been indicated. Comments, in context, related to the interval have been made, for example, that such an interval would capture the population median most of the time.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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