Answering Questions and Defending Your Reasoning

"My 40 students are a sample from the 240 Grade 12 students. Dividing by n − 1 gives a better estimate of the population's spread; dividing by n would slightly underestimate it."

Agree: "Exactly, and I don't claim cause. My survey is observational, so I describe an association. Lurking variables like family responsibilities could play a role. A longitudinal study would get closer to cause."

Give more detail on how something was done. Example: explaining exactly how surveys were distributed by the office in sealed envelopes and collected in a locked box, so no one could connect answers to names.

It confirms you understood, lets the whole audience hear the question, and gives you a moment to think.

Say her data cannot answer it (the sample represents only Pinecrest's Grade 12 students), then say how one could find out (for example, national survey data or samples from other provinces).

Listen, restate, answer with evidence, check.

To agree openly that a criticism is valid.

About 30 to 60 seconds.

Claim (position), evidence (facts or numbers), reasoning (how the evidence supports the claim).

Yes, when followed by how you would find out.

"With 22 points r is less precise than with hundreds, so I describe it only as moderate. But the pattern is clear in the scatter plot, the residuals show no curve, and the negative direction agrees with the comparison of the two groups. I'd still like a larger sample to pin the slope down."

"From my background research: the Canadian 24-Hour Movement Guidelines recommend 8 to 10 hours for youth aged 14 to 17. Most of my population is 17, so I used the lower end, 8 hours, and defined 'meets the guideline' as reporting 8 or more hours on a usual school night."

"Expected value is the long-run average, not an exact prediction. Random variation means 300 plays rarely give exactly 225. A difference of 5 tickets is small compared with the variation: for example, one extra double six changes the payout by 20 tickets. The counts of doubles were within one standard deviation of their expected values, so the data agree with the theory."

Acknowledge it immediately ("Thank you, that's a typo; the median is 7.5"), note that the conclusion is unchanged (the no-job median is 8.5), and correct the slide and report afterwards.

Sample: "Your poll says 55% ± 15%. Could the true proportion actually be below 50%? What would it take to know for sure?" (A good answer: yes, the interval runs from about 40% to 70%; a larger sample would narrow it.)

Amira's population is Grade 12 only, so age varies little (mostly 17, some 18). The design already holds grade constant, which makes age an unlikely explanation for a 68-minute difference. The critic's idea would matter in a study mixing grades; in that case, analysing each grade separately (stratifying) would address it.

The shuffle does not invent values: it uses the real 40 sleep values and only rearranges the group labels. It shows what differences arise if the labels have no connection to sleep (the null statement). Comparing the real difference with this chance distribution measures how surprising the real result would be if job status did not matter. It is a probability model built from the data themselves.

Compare the recorded values of each group: if workers rounded down to whole hours, their answers would cluster at values like 7.0 and 8.0 with few quarter hours. Amira can count how many answers in each group are whole numbers versus quarter or half hours. In the example data, the job group has 15 non-whole values out of 22, which does not suggest heavy rounding down. She could also note that rounding to the nearest hour moves values both up and down, so it would not create a one-directional gap of over an hour.