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Algebra 2 9-12 / Week 12 / Tuesday
2/6
Week 12 · Seedling Heights and the Open House

Tuesday

Survey, experiment, observation
// From a sample to the whole bench
⏱ about 20 min

Tuesday: Survey, Experiment, Observation

"Three things we did this spring," Wren says, chalking three columns. "And three different kinds of claim."

"We drew 10 cells from a cup and measured them," Comet says. "To describe the whole bench. A sample survey."

"We split a tray at random, misted half daily and half weekly, and compared. We assigned the misting. An experiment."

"And we noticed the seedlings by the glass looked taller," Comet says. "We did not move anyone. We just looked."

Nova lights the third column. "Would you like a hint? That one is an observational study, and it is the weakest for cause."

"Because the glass-side seedlings might differ in other ways too," Wren says. "Older, or a different seed packet."

"Random choosing for the survey, random assigning for the experiment, nothing assigned for the observation," Comet says. "What do you notice? Chance does the fair work."

Three kinds of study

KindWhat the crew doesWhere chance comes inWhat it can claim
Sample surveymeasures a part of a groupthe sample is chosen at randoma description of the whole group, with a margin of error
Experimentassigns treatments and comparestreatments are assigned at randomthat the treatment made a difference
Observational studywatches groups that already differnone; nothing is assignedthat two things are linked, not that one caused the other

Statistics is a process: pick a sample by chance, measure it, and reason carefully back to the whole group.

The number for the whole group, like the bench's true mean height, is called a parameter. The sample's number is an estimate of it.

Random choosing keeps a survey fair: no seedling is favored. Random assigning keeps an experiment fair: the two trays start alike except for the treatment.

An observational study has no assignment, so a difference between its groups might come from anything that already differed.

Two ways to test the misting idea

  • Way 1, an experiment: pick 20 cells, flip a coin for each, mist heads daily and tails weekly. Compare. A difference points to the misting.
  • Way 2, an observation: find cells that happened to get more mist from the leaky hose and compare them with the rest. A difference might be the mist, or the hose's corner of the bench.
  • Both are honest if they are labeled honestly. Only the experiment may say the misting made the difference.
WHICH KIND OF STUDY?
  • Read the question.
  • Tap your answer.
The crew drew 10 cell numbers from a cup and measured those seedlings to estimate the bench's mean height. What kind of study is this?
The crew flipped a coin for each of 20 cells, misted heads daily and tails weekly, then compared sprout counts. What kind of study is this?
The crew compared the heights of seedlings that happened to sit by the glass with those further in. What kind of study is this?
Nova picked 30 cells at random from the whole Glass House and recorded how many had sprouted. What kind of study is this?
CHANCE DOES THE FAIR WORK
  • Read the question.
  • Tap your answer.
In a sample survey, what is chosen at random?
In an experiment, what is assigned at random?
Which kind of study may say that a treatment caused a difference?
The bench's true mean height, the number for the whole group, is called a what? Type one word.
WHY THIS EXERCISEKeeping the sample's estimate and the group's parameter apart is the heart of inference.
StatementTrue or false?
A sample survey can describe a whole group from a random part of it.?
An observational study assigns treatments at random.?
In an experiment, random assignment makes the groups alike before the treatment.?
Noticing that glass-side seedlings are taller proves the glass made them taller.?
WHY THIS EXERCISEEach kind of study earns a different kind of sentence. Using the right sentence is what makes a report honest.
Try it
Write one question about your own home that a survey could answer, one an experiment could, and one you could only observe.
For each, write where chance would come in.
Draw three boxes labeled survey, experiment and observation. In each, sketch where the coin or the cup is used.

Clear thinking. Tomorrow is Lab day: you flip coins to see what chance alone produces, and decide whether a tray is surprising.

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