Week 11 — Confidence Intervals for a Mean

Welcome to your Week 11 Start Here page.

Why this matters

One average always comes with a wobble. A public-health team reporting clinic wait times and a field biologist reporting a penguin species' typical mass both owe readers a range, not a lone number.

In plain language

When you measure a sample, its average is a good guess for the whole group, but it is never exactly right. This week you learn to report a confidence interval (a range of believable values for the group's true average, with a stated level of trust) instead of a single number. You will see why the range is built the way it is and how to compute it by hand and with a spreadsheet. You will also learn to say what the range means in plain words, and what it does not mean. Getting that sentence right is the main skill of the week.

• Already covered: Weeks 1 to 10 built description, probability, the normal model, and the sampling distribution of the mean.
• This week: point and interval estimates, the t distribution, and the one-sample t interval.
• How they connect: last week's standard error becomes this week's margin of error.
• Where we're going next: Week 12 builds the same kind of interval for a proportion.

Focus

How far off might one sample's average be, and how do you report that honestly?

By the end of this module, you should be able to:

• [ ] find the degrees of freedom and the critical value t*
• [ ] check the conditions for a one-sample t interval
• [ ] build a 95% t interval by hand and by spreadsheet
• [ ] say what "95% confident" does and does not mean

To-do

Plan your week

1. Read Chapter 11 (about 50 minutes), then the lecture and slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Data Lab (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: build the 95% t interval for the mean Adelie body mass and state it in one correct sentence.

You've got this

Say the interpretation sentence out loud every time, and ask your instructor early if a step snags.

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