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Assessment Report
New Zealand Scholarship
Statistics 2017
Standard 93201
Part A: Commentary
Most candidates made reasonable attempts in each question. Candidates forgot in many cases to start questions on a new page. Also, the standard of writing was poor in many cases which made it difficult to read candidates’ answers. Some candidates resorted to writing in the margins when there were still plenty of blank pages to write on.
Part B: Report on performance standard
Candidates who were awarded Scholarship with Outstanding Performance commonly:
 suggested and explained the effect other variables might have on data, describing the expected relationship
 formed a conclusion from bootstrap inference results, including interpreting the difference between means, a confidence interval, and whether there was sufficient evidence of a difference between the means of the two groups
 connected the percentage and the annual mean number of crashes in 2(b). Hence, they were able to calculate the average mean number of fatal road crashes that didn’t involve alcohol as a factor
 calculated seasonality for Tuesdays in 2(d) realising that seasonal component can be related to days of the week
 calculated conditional probabilities, proved statistical independence, and determined relative risk
 discussed assumptions of different models
 recognised the mix of binomial and normal probabilities in the one question
 provided detailed descriptions and demonstrated understanding of experimental design features
 described and showed understanding of the randomisation test for experiments in their descriptions
 understood sampling variability, margin of error and how confidence intervals are constructed and interpreted
 described the meaning of “statistical significance”
 worked out the conditional probability correctly in Q5 (b) (iii).
Candidates who were awarded Scholarship commonly:
 interpreted a scatter graph in detail (association, strength, direction and scatter), and were able to recognise and describe subgroups. They included the key word of linear in their descriptions
 interpolated or extrapolate and also round their predictions appropriately
 included the mean in their description of confidence intervals
 made relevant statistical points from the time series graphs
 interpreted and described statistical reports, including graphs
 explained how the given information affected the trend and supply further information in Q2 (c)
 converted word problems into either twoway tables or tree diagrams
 knew how to test for statistical independence
 confirmed the normality of the data in Q3 beyond just calculating the mean and standard deviation
 understood the design characteristics in Q4 and were able to answer (a) to (d) correctly
 showed some understanding of randomisation test for experiments but were unable to describe fully enough
 interpreted the graphs correctly in Q5 and provided the required observations and comparisons
 recognised that conditional probability was involved in Q5 (b) and worked out the correct answer
 got Q5 (b) (iii) partly correct. Not many used the 18% or the 83%. Common error was to assume equal proportion of men and women and so produce 0.775 as a denominator.
Other candidates
Candidates who were not awarded Scholarship commonly:
 were unable to interpret a scatter graph (association, strength and direction) fully enough
 were unable to form a conclusion from the bootstrap inference results and conclude whether there was sufficient evidence of a difference between the means of the two groups
 were unable to extract a variety of observations from time series graphs
 were unable to recognise which probability distribution was applicable in solving a probability problem
 were unable to interpret or describe statistical reports fully enough, including graphs
 were unable to correctly covert word problems into either twoway tables or tree diagrams
 had difficulty in describing their assumptions and were satisfied in many instances with giving a vague answer with no context
 did not know or were unable to describe completely experimental design features. Their explanations were too brief and nonspecific in many instances
 did not recognise the randomisation test for experiments and when it should be applied
 did not answer as the question was posed in Q5. They made statements about percentages but did not give the meaning of these numbers. In (iii) many answers lacked details on exactly how the graph was going to be constructed with no explanation
 had no idea of “sampling variability” or “margin of error”.
Performance standard specific comment
The overall distribution of marks for each question was as follows:
Question  Percentage in Range  
 0 to 4  5 to 6  7 to 8 
1  41.3  40.0  18.7 
2  76.0  20.0  4.0 
3  44.9  31.9  23.2 
4  37.9  34.4  27.7 
5  71.1  22.9  6.0 
The most welldone questions were Q1, Q3 and Q4 where 59%, 55% and 62% of candidates respectively achieved scholarship standard. In Q3 and Q4, 23% and 28% of candidates respectively achieved outstanding standard. The most difficult question was Q2 where only 24% achieved scholarship standard.
Subject page
Previous years' reports
2016 (PDF, 197KB)