NCEA Level 3 Mathematics and Statistics 91584 (3.12) — page 1 of 6

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 key features in reports relevant to any conclusions made in those reports. / Evaluate statistically based reports, with justification involves supporting the comments made by referring to statistical evidence and processes used in reports, relevant to conclusions made in those reports. / Evaluate statistically based reports, with statistical insight involves integrating statistical and contextual information to assess the quality of reports with respect to conclusions made in those reports.

Evidence Statement

One / Expected Coverage / Achievement / Merit / Excellence
(a) (i)
and
(a) (ii) / The margin of error is 1/√200 (using the rule of thumb 1/√n)
= 7.1%
The 95% confidence interval for a survey percentage of 53% is
[45.9% , 60.1%].
As this confidence interval includes percentages less than 50%, the claim is not supported.
The survey percentage would need to be at least 57.1% to have evidence to support the claim that most (the majority) of New Zealand mothers have accessed their children’s Facebook page, as this would provide a 95% confidence interval of [50% , 64.2%].
Note: The formula could also be used to calculate the margin of error. / The margin of error is calculated and used to calculate a confidence interval. / The confidence interval is calculated and interpreted as part of the explanation that the claim is supported.
The margin of error is calculated and used to determine the lowest survey percentage to allow a claim to be made.
(b) (i) / The rule of thumb (1/√n) should only be used as an estimate of the margin of error with survey percentages between approximately 30% and 70% – which excludes (USA and) Japan. For Japan, the survey percentage is well outside this range. The margin of error for the survey percentage for Japan would be much smaller than the ‘rule of thumb’ margin of error of 1/√400. / Survey percentages for which the ‘rule of thumb’ should not be used are identified. / At least one country is identified being unsuitable to use the ‘rule of thumb’ and a partial explanation is given regarding the size of the associated margin of error. / At least one country is identified being unsuitable to use the ‘rule of thumb’ and a full explanation is given 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 percentage of Japanese parents are Facebook users and hence it is only possible for a very small percentage of Japanese parents to be Facebook ‘friends’ with their children. / Partial explanation is given about how the survey percentages could be affected by the percentage of Facebook users within a country. / Full explanation is given about how the survey percentages could be affected by the percentage of Facebook users within a country.
(c) / The study was funded by AVG – a company that sells products concerned with internet security. This survey is about concerns about using technology, in particular internet-based activities, eg downloading illegal music, and educating teenagers about using the internet responsibly. A desire to encourage parents to buy their products could motivate AVG to produce findings that suggest the internet is unsafe. / The link is identified between the funding of the research by an internet-related company and the survey being about internet-related activity. / The link between the funding of the research by an internet-related company and the survey being about internet-related activity is 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 made from this sample, it should be a random sample of all New Zealand cat and dog owners and / or it should be representative of all New Zealand cat and dog owners. The sample should contain cat and dog owners from both rural and urban areas of New Zealand, proportional to the number of pet owners in these areas. The ratio of dog and cat owners should be around 5 : 3 in the sample.
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. / The target population is identified.
One characteristic of the sample is identified, eg it is randomly selected or it is representative. / The target population is identified and at least one characteristic of the sample is described in context and linked to representativeness.
(b) / A potential difficulty could be about how respondents of the survey interpret the words ‘keeping to yourself’ – a clear definition of what ‘keeping to yourself’ means would need to be provided for people completing the survey so that respondents were interpreting these words in a consistent way.
Note: Other potential difficulties are possible. / A potential difficulty with the question is identified.
(c) / The 400 respondents could be split into 250 cat owners and 150 dog owners.
Margin of error for cat owners = 1/√250 = 6.32%
Margin of error for dog owners = 1/√150 = 8.16%
Average margin of error = 7.2%
Comparing two subgroups so margin of error for comparison = 1.5 x 7.2% = 10.8%
The difference between the two survey percentages is 61% - 53% = 8 percentage points.
The 95% confidence interval for the difference between the two survey percentages is [-2.8%, 18.8%].
With 95% confidence, I estimate that the percentage of New Zealand cat owners who prefer to ‘keep to themselves’ is somewhere between 2.8% lower and 18.8% higher than the corresponding percentage of New Zealand dog owners. This means the evidence presented in the report could not be used to support the claim that a higher percentage of New Zealand cat owners prefer to ‘keep to themselves’ than New Zealand dog owners.
Note: The formula could also be used to calculate the margin of error for the confidence interval. / Margin of errors of each group (New Zealand cat owners and New Zealand dog owners) correctly calculated. / The margin of errors of each group are calculated and used to construct a confidence interval for the difference between the proportion of New Zealand cat owners and New Zealand dog owners who prefer to ‘keep to themselves’. / The confidence interval for the difference between the proportion of New Zealand cat owners and New Zealand dog owners who prefer to ‘keep to themselves’ is constructed by calculating and using the margin of errors of each group and is interpreted as part of the explanation as to whether the evidence could support the claim.
(d) / There are likely to be pet owners who own both cats and dogs, as well as other pets. People may also own more than one cat and / or dog. We do not know whether the question used had a ‘both’ option or if there were any other options about owning other pets or owning more than one cat or dog (question effect). This might be a problem as it could bias survey responses and it might be that the number of pets owned is what explains your relationship status (this might be the explanation for a higher proportion of cat owners 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. / Two potential non-sampling errors, biases, or issues are identified. / Two potential non-sampling errors, biases, or issues are identified and described by relating to the evidence or processes presented in the report. / Two potential non-sampling errors, biases, or issues are identified and discussed, supported with statistical and contextual reasoning.
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.
Hours of sleep is measured by the time the child was in bed. This would not be the same as hours of sleep (time in bed would be longer than hours of sleep). The measuring of time in bed would rely on parents logging the time in bed themselves or being asked to recall it at a later date by the researcher, which means there may be inaccuracy in this measurement. To measure hours of sleep accurately would require watching the child throughout the night, which is unpractical.
Note: Either number of hours sleep or time in bed is acceptable for the explanatory variable. / Both variables are identified. / Both variables are identified
AND
one potential issue with the measurement of the explanatory variable is stated. / Both variables are identified
AND
one potential issue with the measurement of the explanatory variable is discussed, supported with statistical and contextual reasoning.
(b) / This is an observational study as the number of hours of sleep was not controlled by the researchers – it would not be possible for the researcher to dictate how many hours of sleep each child had per night. The children were observed as a group over a period of time. Because this is an observational study, causal relationship claims should not be made, or should at least be made with extreme care. / Identification that this study is an observational study. / Explanation given of why this is an observational study (which links to the context) and the limitation 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 ‘equals’ could be replaced with the words ‘leads to’ or ‘means’. / Identification of a causal claim in statement.
(d) / The amount of exercise that the child had during childhood could also be associated with the adult body mass index, eg more hours of exercise during childhood could cause lower adult body mass index.
The amount of food eaten by the participants as adults could also be associated with the adult body mass index, eg larger amounts of food eaten could increase adult body mass index. / Two related lifestyle factors are identified. / Two related lifestyle factors are identified and partial explanations are given as to how these might affect the adult body mass index. / Two related lifestyle factors are identified and full explanations are given as to how 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.