91584 Sample Assessment Schedule



SAMPLE ASSESSMENT SCHEDULE

Mathematics and Statistics 91584 (3.12): Evaluate statistically based reports

Assessment Criteria

|Achievement |Achievement with Merit |Achievement with Excellence |

|Evaluate statistically based reports involves identifying and commenting on |Evaluate statistically based reports, with justification involves supporting|Evaluate statistically based reports, with statistical insight involves |

|key features in reports relevant to any conclusions made in those reports. |the comments made by referring to statistical evidence and processes used in|integrating statistical and contextual information to assess the quality of |

| |reports, relevant to conclusions made in those reports. |reports with respect to conclusions made in those reports. |

Evidence Statement

|One |Expected Coverage |Achievement |Merit |Excellence |

|(a) (i) |The margin of error is 1/√200 (using the rule of thumb 1/√n) |The margin of error is calculated|The confidence interval is | |

|and |= 7.1% |and used to calculate a |calculated and interpreted as part | |

|(a) (ii) |The 95% confidence interval for a survey percentage of 53% is |confidence interval. |of the explanation that the claim | |

| |[45.9% , 60.1%]. | |is supported. | |

| |As this confidence interval includes percentages less than 50%, the claim is not supported. | |The margin of error is calculated | |

| |The survey percentage would need to be at least 57.1% to have evidence to support the claim that most (the| |and used to determine the lowest | |

| |majority) of New Zealand mothers have accessed their children’s Facebook page, as this would provide a 95%| |survey percentage to allow a claim | |

| |confidence interval of [50% , 64.2%]. | |to be made. | |

| |Note: The formula [pic] could also be used to calculate the margin of error. | | | |

|(b) (i) |The rule of thumb (1/√n) should only be used as an estimate of the margin of error with survey percentages|Survey percentages for which the |At least one country is identified |At least one country is |

| |between approximately 30% and 70% – which excludes (USA and) Japan. For Japan, the survey percentage is |‘rule of thumb’ should not be |being unsuitable to use the ‘rule |identified being unsuitable to |

| |well outside this range. The margin of error for the survey percentage for Japan would be much smaller |used are identified. |of thumb’ and a partial explanation|use the ‘rule of thumb’ and a |

| |than the ‘rule of thumb’ margin of error of 1/√400. | |is given regarding the size of the |full explanation is given |

| | | |associated margin of error. |regarding the size of the |

| | | | |associated margin of error. |

|(b) (ii) |A possible explanation, for example, for Japan’s relatively low survey percentage is that a very small | |Partial explanation is given about |Full explanation is given about |

| |percentage of Japanese parents are Facebook users and hence it is only possible for a very small | |how the survey percentages could be|how the survey percentages could|

| |percentage of Japanese parents to be Facebook ‘friends’ with their children. | |affected by the percentage of |be affected by the percentage of|

| | | |Facebook users within a country. |Facebook users within a country.|

|(c) |The study was funded by AVG – a company that sells products concerned with internet security. This survey |The link is identified between |The link between the funding of the| |

| |is about concerns about using technology, in particular internet-based activities, eg downloading illegal |the funding of the research by an|research by an internet-related | |

| |music, and educating teenagers about using the internet responsibly. A desire to encourage parents to buy |internet-related company and the |company and the survey being about | |

| |their products could motivate AVG to produce findings that suggest the internet is unsafe. |survey being about |internet-related activity is | |

| | |internet-related activity. |explained in terms of the possible | |

| | | |motivation for results. | |

|Not Achieved |NØ |No response; no relevant evidence. |

| |N1 |Candidate gives a partial response to ONE part of the question. |

| |N2 |Candidate gives partial responses to TWO parts of the question. |

|Achievement |A3 |Candidate gives ONE opportunity from the Achievement criteria. |

| |A4 |Candidate gives TWO opportunities from the Achievement criteria. |

|Merit |M5 |Candidate gives ONE opportunity from the Merit criteria. |

| |M6 |Candidate gives TWO opportunities from the Merit criteria. |

|Excellence |E7 |Candidate gives ONE opportunity from the Excellence criteria. |

| |E8 |Candidate gives TWO opportunities from the Excellence criteria. |

|Two |Expected Coverage |Achievement |Merit |Excellence |

|(a) |The target population for this survey is New Zealand cat and dog owners. In order for inferences to be |The target population is |The target population is identified| |

| |made from this sample, it should be a random sample of all New Zealand cat and dog owners and / or it |identified. |and at least one characteristic of | |

| |should be representative of all New Zealand cat and dog owners. The sample should contain cat and dog |One characteristic of the sample |the sample is described in context | |

| |owners from both rural and urban areas of New Zealand, proportional to the number of pet owners in these |is identified, eg it is randomly |and linked to representativeness. | |

| |areas. The ratio of dog and cat owners should be around 5 : 3 in the sample. |selected or it is representative.| | |

| |Note: Other characteristics of the sample are possible as long as they are clearly linked to the target | | | |

| |population. It is acceptable to refer to New Zealand cat owners as one population and New Zealand dog | | | |

| |owners as another population. | | | |

|(b) |A potential difficulty could be about how respondents of the survey interpret the words ‘keeping to |A potential difficulty with the | | |

| |yourself’ – a clear definition of what ‘keeping to yourself’ means would need to be provided for people |question is identified. | | |

| |completing the survey so that respondents were interpreting these words in a consistent way. | | | |

| |Note: Other potential difficulties are possible. | | | |

|(c) |The 400 respondents could be split into 250 cat owners and 150 dog owners. |Margin of errors of each group |The margin of errors of each group |The confidence interval for the |

| |Margin of error for cat owners = 1/√250 = 6.32% |(New Zealand cat owners and New |are calculated and used to |difference between the |

| |Margin of error for dog owners = 1/√150 = 8.16% |Zealand dog owners) correctly |construct a confidence interval for|proportion of New Zealand cat |

| |Average margin of error = 7.2% |calculated. |the difference between the |owners and New Zealand dog |

| |Comparing two subgroups so margin of error for comparison = 1.5 x 7.2% = 10.8% | |proportion of New Zealand cat |owners who prefer to ‘keep to |

| |The difference between the two survey percentages is 61% - 53% = 8 percentage points. | |owners and New Zealand dog owners |themselves’ is constructed by |

| |The 95% confidence interval for the difference between the two survey percentages is [-2.8%, 18.8%]. | |who prefer to ‘keep to themselves’.|calculating and using the margin|

| |With 95% confidence, I estimate that the percentage of New Zealand cat owners who prefer to ‘keep to | | |of errors of each group and is |

| |themselves’ is somewhere between 2.8% lower and 18.8% higher than the corresponding percentage of New | | |interpreted as part of the |

| |Zealand dog owners. This means the evidence presented in the report could not be used to support the claim| | |explanation as to whether the |

| |that a higher percentage of New Zealand cat owners prefer to ‘keep to themselves’ than New Zealand dog | | |evidence could support the |

| |owners. | | |claim. |

| |Note: The formula [pic] could also be used to calculate the margin of error for the confidence interval. | | | |

|(d) |There are likely to be pet owners who own both cats and dogs, as well as other pets. People may also own |Two potential non-sampling |Two potential non-sampling errors, |Two potential non-sampling |

| |more than one cat and / or dog. We do not know whether the question used had a ‘both’ option or if there |errors, biases, or issues are |biases, or issues are identified |errors, biases, or issues are |

| |were any other options about owning other pets or owning more than one cat or dog (question effect). This |identified. |and described by relating to the |identified and discussed, |

| |might be a problem as it could bias survey responses and it might be that the number of pets owned is what| |evidence or processes presented in |supported with statistical and |

| |explains your relationship status (this might be the explanation for a higher proportion of cat owners | |the report. |contextual reasoning. |

| |being single). | | | |

| |There may be a potential issue if only Purina customers were used for the survey (selection bias), as the | | | |

| |people who buy Purina cat or dog food might not be representative of all New Zealand pet owners. For | | | |

| |example, if Purina customers are mostly older people, they may own cats as companions as they are easier | | | |

| |to look after than dogs, rather than using them ‘as a substitute for a significant other’ as stated in the| | | |

| |report. Additionally, any inferences made could only be applied to Purina customers, not necessarily all | | | |

| |New Zealand pet owners. | | | |

| |Note: Other potential non-sampling errors, biases, or issues are possible. | | | |

|Not Achieved |NØ |No response; no relevant evidence. |

| |N1 |Candidate gives a partial response to ONE part of the question. |

| |N2 |Candidate gives partial responses to TWO parts of the question. |

|Achievement |A3 |Candidate gives ONE opportunity from the Achievement criteria. |

| |A4 |Candidate gives TWO opportunities from the Achievement criteria. |

|Merit |M5 |Candidate gives ONE opportunity from the Merit criteria. |

| |M6 |Candidate gives TWO opportunities from the Merit criteria. |

|Excellence |E7 |Candidate gives ONE opportunity from the Excellence criteria. |

| |E8 |Candidate gives TWO opportunities from the Excellence criteria. |

|Three |Expected Coverage |Achievement |Merit |Excellence |

|(a) |The explanatory variable is hours of sleep and the response variable is the body mass index. |Both variables are identified. |Both variables are identified |Both variables are identified |

| |Hours of sleep is measured by the time the child was in bed. This would not be the same as hours of sleep| |AND |AND |

| |(time in bed would be longer than hours of sleep). The measuring of time in bed would rely on parents | |one potential issue with the |one potential issue with the |

| |logging the time in bed themselves or being asked to recall it at a later date by the researcher, which | |measurement of the explanatory |measurement of the explanatory |

| |means there may be inaccuracy in this measurement. To measure hours of sleep accurately would require | |variable is stated. |variable is discussed, supported|

| |watching the child throughout the night, which is unpractical. | | |with statistical and contextual |

| |Note: Either number of hours sleep or time in bed is acceptable for the explanatory variable. | | |reasoning. |

|(b) |This is an observational study as the number of hours of sleep was not controlled by the researchers – it|Identification that this study is |Explanation given of why this is an| |

| |would not be possible for the researcher to dictate how many hours of sleep each child had per night. The|an observational study. |observational study (which links to| |

| |children were observed as a group over a period of time. Because this is an observational study, causal | |the context) and the limitation | |

| |relationship claims should not be made, or should at least be made with extreme care. | |this has on making a causal | |

| | | |relationship claim. | |

|(c) |The word ‘equals’ in the statement is misleading as it implies a causal relationship, eg the word |Identification of a causal claim in| | |

| |‘equals’ could be replaced with the words ‘leads to’ or ‘means’. |statement. | | |

|(d) |The amount of exercise that the child had during childhood could also be associated with the adult body |Two related lifestyle factors are |Two related lifestyle factors are |Two related lifestyle factors |

| |mass index, eg more hours of exercise during childhood could cause lower adult body mass index. |identified. |identified and partial explanations|are identified and full |

| |The amount of food eaten by the participants as adults could also be associated with the adult body mass | |are given as to how these might |explanations are given as to how|

| |index, eg larger amounts of food eaten could increase adult body mass index. | |affect the adult body mass index. |these might affect the adult |

| | | | |body mass index. |

|Not Achieved |NØ |No response; no relevant evidence. |

| |N1 |Candidate gives a partial response to ONE part of the question. |

| |N2 |Candidate gives partial responses to TWO parts of the question. |

|Achievement |A3 |Candidate gives ONE opportunity from the Achievement criteria. |

| |A4 |Candidate gives TWO opportunities from the Achievement criteria. |

|Merit |M5 |Candidate gives ONE opportunity from the Merit criteria. |

| |M6 |Candidate gives TWO opportunities from the Merit criteria. |

|Excellence |E7 |Candidate gives ONE opportunity from the Excellence criteria. |

| |E8 |Candidate gives TWO opportunities from the Excellence criteria. |

Note: At any stage, for any question, a candidate may have offered other information that is statistically valid and can be used to replace points raised in the schedule.

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