How do I correctly pose a comparison investigative question for Kiwi Kapers 3 and state my conclusions when making an inference about the population? (3.10)

On comparison questions:

Level 6   I wonder if heights of NZ Yr 11 boys tend to be greater than heights of NZ year 11 girls (looking for a tendency, do the boxes overlap or not, if they do is it too much, level 6)

Level 7  I wonder if the median height of NZ year 11 boys is greater than the median height of NZ year 11 girls (seeing if the informal confidence intervals overlap or not)

Level 8  I wonder what the difference in median heights is between NZ year 11 boys and NZ year 11 girls?   (or something like that, finding an interval for the difference – like a summary situation.  If 0 in the interval then they cannot make the  call.  They could start with the level 7 question, but use the level 8 idea to answer the question).

I am not that keen that they look at differences at level 7.  It is more important that they are now using a parameter (the median) and still looking at tendency, i.e. using an informal confidence interval and if they overlap, they cannot make the call.

On writing conclusions:

Conclusion: Based on these samples I would make the call that the population median height of NZ year 11 boys is greater than the population median height of NZ year 11 girls. That is, I would make the call that NZ year 11 boys tend to be taller than NZ year 11 girls back in the two populations.

Justification: The informal confidence interval for the population median height of NZ year 11 boys is (much) further up the scale than the informal confidence interval for the population median height of NZ year 11 girls and these informal confidence intervals do not overlap. I am quite sure that if I were to take another sample of NZ year 11 boys and another sample of NZ year 11 girls this non-overlapping pattern in confidence intervals for the population medians would persist, thus giving the same conclusion.

[Strictly speaking the last sentence is not a justification for the conclusion made but it would be nice if students articulated this.]

Notes:

We used “further up the scale” rather than “higher” as higher could refer to a single value.

We used “sure” rather than “confident” as we should reserve the use of the term ‘confident’ to ideas about the confidence we have in our interval estimate (i.e. our confidence interval) which is different from the confidence we have about the ‘pattern repeatability’ and we don’t want students to get muddled.