6: Conclusion
How will we answer the question?
Investigative Question
The Conclusion looks back to the Problem and tries to answer the investigative question.
We asked a question like:
I wonder whether the median weight of station wagons is greater than the median weight of hatchbacks across all new cars sold in NZ in 2018?
The Analysis section gave information about the median weight and IQR of weights of a sample of cars from the population.
We used these to calculate informal confidence intervals for the population medians (ICI's) for the median weight in each group of the population.
Now we ask - what does the overlap of the ICI's tell us about the median of each group in the population? Is there enough information to say that one population median is larger than the other?
Overlap
If the informal confidence intervals for the population medians overlap, then we can't be sure that one is bigger than the other.
From this sample, we can be fairly certain that the median weight of a new grey car in NZ in 2018 is between 1882 and 1994 kg.
On the other hand, we can be fairly certain that the median weight of a new silver car in NZ in 2018 is between 1829 and 1941 kg.
Because these two ICI's overlap, this sample does not give us enough evidence to say that the median weight of a new grey car is greater than the median weight of a new silver car in the population of all new NZ cars in 2018.
No Overlap
If the informal confidence intervals for the population medians do not overlap, then we can be fairly sure that one is bigger than the other.
From this sample, we can be fairly certain that the median weight of a new red car in NZ in 2018 is between 1784 and 1894 kg.
On the other hand, we can be fairly certain that the median weight of a new white car in NZ in 2018 is between 1999 and 2101 kg.
Because these two ICI's do not overlap, this sample gives us enough evidence to say that the median weight of a new red car is greater than the median weight of a new white car in the population of all new NZ cars in 2018.
Context
It should be crystal clear what the answer is to the investigative question that was first stated in the Problem.
The Conclusion finishes off the report, by presenting evidence that answers the investigative question. Is there enough evidence to say "yes, there's probably a difference in the population"?
All of the Conclusion should be in context. It isn't about medians and ICI's, it's about whether we know enough about the median weights of new station wagons and hatchbacks in our small sample to infer anything about ALL new cars in NZ in 2018.
Your Problem section may have made an hypothesis about the context. Your Conclusion should only address the investigate question.
Read the Achieved Exemplar to see what is expected at this level for the Conclusion.
Use the Achieved Exemplar as a template to write the Conclusion for Worksheet 9.
Inf Worksheet 9.pdfAchieved Exemplar.pdf