Week 11 Data Lab: Three Species, Three Intervals

Part 1 — The Big Picture

This week you learned to turn one sample mean into a confidence interval: find the degrees of freedom and t*, compute the standard error and the margin of error, check the conditions, and say what the interval means. In this lab you do it yourself on real data, three times. You open the penguin field log, build a 95% t interval for the mean body mass of each of the three species, check your Adelie interval against the one in the chapter, and line the three intervals up to see which species' means look alike and which stand apart. Then you check a chatbot's answers about the same data.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: What do 95% t intervals for the mean body mass of the Adelie, Chinstrap, and Gentoo penguins tell us about how the three species compare, and what do they not tell us?

Workshop data: palmer-station-penguins

Get the data: palmer-station-penguins landing page or the direct data file — free, no login required.

Source: Measurements of 344 penguins of three species on three islands of Antarctica's Palmer Archipelago, recorded by field researchers and republished in the palmerpenguins package.

• Rows: 344 penguins
• Columns: species, island, bill_length_mm, bill_depth_mm, flipper_length_mm, body_mass_g, sex, year
• Missing values: Numeric measurement columns and sex carry missing values for a small number of penguins

Part 3 — Materials & Procedure

Tools and materials

• Google Sheets (free) or Excel
• The palmerpenguins CSV file
• A document or notebook for your written answers

Ways of working

• interpret-real-data
• compute-and-plot
• structured-observation

Procedure

1. Open a blank sheet and name the first tab Penguins. In cell A1 type =IMPORTDATA("https://raw.githubusercontent.com/allisonhorst/palmerpenguins/main/inst/extdata/penguins.csv"). In Excel, save the file from that address, then use Data, then From Text/CSV, and load it starting in cell A1. Tool: Google Sheets (free) or Excel. Check: Row 1 shows the eight column names, the penguins fill rows 2 through 345, and body mass sits in column F.
2. Add a tab named Masses. In A1 type =FILTER(Penguins!F2:F345, Penguins!A2:A345="Adelie", Penguins!F2:F345<>"NA"). In B1 use the same formula with "Chinstrap", and in C1 with "Gentoo". Each column now lists one species' recorded body masses. Tool: Google Sheets (free) or Excel. Check: Three columns of whole numbers of grams appear, one per species, with no NA entries.
3. Fill the first scaffold table. In rows 202 to 205 of each column, below the rows the formulas read, type =COUNT(A1:A200), =AVERAGE(A1:A200), and =STDEV(A1:A200), changing the letter for each species, and then =STDEV(A1:A200)/SQRT(COUNT(A1:A200)) for the standard error. Round each to two decimals only when you copy it into the table. Tool: Google Sheets (free) or Excel. Check: The counts are 151, 68, and 123, and each standard error is a few tens of grams, far smaller than its standard deviation.
4. Fill the second scaffold table. For each species, the degrees of freedom are its count minus 1. In rows 206 and 207 of each column, type =T.INV.2T(0.05, COUNT(A1:A200)-1) for t*, =CONFIDENCE.T(0.05, STDEV(A1:A200), COUNT(A1:A200)) for the margin of error, and then the mean minus the margin and the mean plus the margin for the two ends. Tool: Google Sheets (free) or Excel. Check: Each t* sits a little above 1.96, and the Adelie interval matches the chapter's 3,626.92 g to 3,774.40 g, or reads 3,626.93 g at the lower end because the spreadsheet keeps every digit of t*.
5. Draw the three intervals on one number line in grams, by hand or with a chart: mark each species' lower end, mean, and upper end, and label each line with the species name. In a sheet, a line chart with the species across the bottom and the lower end, mean, and upper end as three series shows the same picture. Tool: Google Sheets (free) or Excel. Check: Two intervals sit near 3,700 g and overlap, and one sits far above them, near 5,000 g.
6. Fill the third scaffold table by comparing each pair of intervals: write whether they overlap and what that suggests about the two population means, in words. Check: Each pair has a yes-or-no overlap and a one-sentence reading in the course's careful language.

Fallback route

When to use it: Use this route if the penguin file will not import or no spreadsheet is available.

Work from the model data below, which reports the summaries from the real file and the critical values a t table or calculator gives. Copy the counts, means, and standard deviations into the first scaffold table, compute each standard error as s divided by the square root of n with a calculator, then build each interval by hand: margin of error equals t* times the standard error, and the two ends are the mean minus and plus the margin. Draw the number line by hand. Answer every analysis question and the critique step from these records, and submit the same items for equal credit.

This route earns the same credit as the primary route.

These summaries from the real file and the matching critical values give you every input the lab needs without importing it.

Fallback model data

Quantity	Adelie	Chinstrap	Gentoo
Count with a recorded mass, n	151	68	123
Sample mean, x̄ (g)	3,700.66	3,733.09	5,076.02
Sample standard deviation, s (g)	458.57	384.34	504.12
Degrees of freedom	150	67	122
Critical value t* for 95%	1.976	1.996	1.980
Standard error (g)

Part 4 — The Scaffold

Summarize each species so you have every input the interval needs.

Student scaffold table 1

Summary	Adelie	Chinstrap	Gentoo
Count with a recorded mass, n
Sample mean, x̄ (g)
Sample standard deviation, s (g)
Standard error, SE = s ⁄ √n (g)

Build each 95% t interval step by step, from the degrees of freedom to the two ends.

Student scaffold table 2

Step	Adelie	Chinstrap	Gentoo
Degrees of freedom, df
Critical value t* for 95%
Margin of error (g)
Lower end (g)
Upper end (g)

Compare the intervals two at a time to see which species' means look alike and which stand apart.

Student scaffold table 3

Pair of species	Do the intervals overlap?	What this suggests about the two population means
Adelie and Chinstrap
Adelie and Gentoo
Chinstrap and Gentoo

Part 5 — Analysis Questions

1. Report the three 95% t intervals from your second table. Compare your Adelie interval with the chapter's 3,626.92 g to 3,774.40 g and explain any difference of a hundredth of a gram.
2. Look at your number line. Which intervals overlap, and which one stands apart? Describe the picture in words, without relying on color.
3. Write the Chinstrap interval in the course sentence, "we are 95% confident that the population mean body mass of Chinstrap penguins is between … and …". Then compare the interval's width with the Chinstrap standard deviation and explain why the interval says nothing about where most single Chinstrap penguins weigh.
4. The Chinstrap masses have a smaller standard deviation than the Adelie masses, yet the Chinstrap interval is wider. Use the levers of the margin of error, the sample size through √n and t*, to explain why.
5. Choose one and answer it in 3–4 sentences. (a) The penguins were weighed in a field study, not drawn at random: what does that mean for how far your three intervals can speak for penguins that were never weighed? (b) The Adelie and Chinstrap intervals overlap: does that prove the two species have the same mean mass? Explain what the overlap does and does not show.

Part 6 — AI-Critique Moment

Choose one equal-credit critique route. Route A: ask an approved AI tool to critique your completed work, then check its response against your own evidence. Route B is the no-AI equivalent printed below.

Approved tools: Claude, Gemini, ChatGPT, Grok, Microsoft Copilot.

Prompt to paste:

I've pasted my completed Week 11 Data Lab tables above. In the lab I used the Palmer penguins file and built a 95% t interval for the mean body mass of each of the three species: 151 Adelie, 68 Chinstrap, and 123 Gentoo penguins with a recorded mass. Please do five things. First, give the 95% confidence interval for the mean Chinstrap body mass and explain what it means. Second, describe the shape of the body masses of all 342 penguins together and name any skew. Third, say whether living on Biscoe Island is what makes Gentoo penguins heavier than the other species. Fourth, suppose each of two penguins picked at random independently has a 0.25 chance of weighing more than 5,000 g; give the chance that exactly one of the two does. Fifth, tell me whether the overlap of the Adelie and Chinstrap intervals proves the two species have the same mean mass.

Test the response for these likely failures:

• Chatbots often say there is a 95% probability that the mean Chinstrap mass lies in the interval, or that 95% of Chinstrap penguins weigh between its two ends.
• Chatbots often state a Chinstrap interval or summary from memory, such as a mean that does not match the file, a made-up sample size, or a z interval with 1.96 in place of t*.
• Chatbots sometimes call the 342 body masses left-skewed because most penguins are on the lighter side, naming the skew by where the pile is.
• Chatbots often say that living on Biscoe Island causes Gentoo penguins to be heavier, reading a cause from an association.
• Chatbots often compute 0.25 × 0.75 = 0.1875 for exactly one heavy penguin and stop, forgetting that the heavy one could be the first pick or the second.

Write 3–5 sentences naming one thing the chatbot got right and at least two places it went wrong or overreached, quoting its words and correcting each with evidence from your own tables or the course's pinned values.

Equivalent route (no AI required)

No AI account is required for this lab. Instead of the chatbot, critique this flawed analysis, printed here in full: "There is a 95% probability that the true mean mass of Chinstrap penguins lies in my interval, and 95% of Chinstrap penguins weigh between its two ends. The 68 Chinstraps average 3,800 g, and with 1.96 standard errors the interval is about 3,709 g to 3,891 g. The body masses of all 342 penguins are left-skewed, because most penguins are on the light side. Living on Biscoe Island makes Gentoo penguins heavier. If each of two penguins has a 0.25 chance of weighing over 5,000 g, the chance that exactly one does is 0.25 × 0.75 = 0.1875. Because the Adelie and Chinstrap intervals overlap, the two species have exactly the same mean mass." Mark it up: quote each flawed sentence, name what is wrong (a misread confidence statement, an invented statistic or the wrong critical value, a wrong skew claim, cause read from association, a dropped number of ways, or an overclaim from overlapping intervals), cite the evidence from your tables or the course's pinned values, and write a corrected sentence beneath it. This route assesses the same objective (Objective 6 — construct and correctly interpret confidence intervals for a population mean and a population proportion, including the meaning of the confidence level and the margin of error) as the chatbot critique, takes comparable effort (about 30 minutes and 200–300 words), is scored by the same scoring criteria for the same credit, and its own submission artifact is the marked-up flawed analysis, posted in place of the chatbot share link and report.

Part 7 — What to Submit

• All three completed scaffold tables
• Your number line of the three intervals, as a chart or a labelled sketch, or a written description of it
• Written answers to all five analysis questions
• The chatbot critique report with its share link, or the equivalent route's marked-up flawed analysis

Deliverable:

A short Data Lab report on the three species: three completed tables (each species' count, mean, standard deviation, and standard error; each 95% t interval from the degrees of freedom to the two ends; and a pairwise comparison of the intervals), a number line of the three intervals as a chart or a labelled sketch or a written description, written answers to five analysis questions, and a critique of a chatbot's answers about the same data, or, on the equivalent route, a marked-up correction of the printed flawed analysis. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text. Choose a written, recorded, or visual form for your answers; every form is graded by the same scoring criteria.

Rubric

The rubric below shows how each submitted part is evaluated; bands are full, partial, or none.

Workshop evaluation criteria

Criterion	Full	Partial	None
Importing and summarizing the three species	The count, mean, standard deviation, and standard error are recorded for all three species with the right group sizes, from the file or the fallback model data, and each standard error divides by the square root of the count.	The summaries are present, but one or two values are missing, use the wrong group, include the NA entries, or divide by the count instead of its square root.	No summaries are recorded, or the values are invented rather than computed.
Building the three intervals	All three intervals show the degrees of freedom, t* for 95%, the margin of error, and both ends, and analysis question 1 checks the Adelie interval against the chapter's and explains a one-hundredth difference as rounding of t*.	The intervals are mostly complete, but a step is missing or wrong, such as degrees of freedom equal to the count or z* in place of t*, or the Adelie check is left out.	The interval table is missing or not built from the data.
Comparing and interpreting the intervals	Analysis questions 2, 3, and 4 describe which intervals overlap, write the Chinstrap interval in the course sentence about the population mean, contrast its width with the spread of single birds, and explain the wider Chinstrap interval through the sample size, √n, and t*.	The comparison or the interpretation is attempted, but the sentence puts the 95% on one interval or on the birds, or the width explanation leaves out the sample size.	Analysis questions 2 to 4 are missing or do not use the student's own tables.
Critique of the chatbot or of the printed flawed analysis	On either route, at least two errors are quoted and corrected with evidence from the student's own tables or the course's pinned values, including the misread confidence statement, and one correct point is acknowledged; both routes earn this band equally.	On either route, errors are named but corrected without evidence, or only one error is caught.	No critique appears, or pasted output is submitted without any checking.
Reflection on what the intervals can and cannot show	The chosen reflection option is answered in 3–4 sentences that name a specific limit, such as a field sample that was not drawn at random or overlapping intervals that do not prove equal means.	The reflection names a limit in general terms without tying it to this lab's intervals.	No reflection is submitted.

Quality Gate

• Every count, mean, standard deviation, and interval end comes from your own formulas or the fallback model data, never from memory or a chatbot.
• Each standard error divides the standard deviation by the square root of that species' count, not by the count itself.
• Each interval uses t* for 95% with that species' count minus 1 degrees of freedom.
• Every interpretation is about the population mean, uses the course sentence, and never says that 95% of the penguins fall in the interval.
• The number line, chart, or description labels each species and the grams axis in words.
• No statistic, count, or source is invented anywhere in the submission.
• The critique quotes the chatbot or the flawed analysis and corrects at least two errors with evidence from your tables or the course's pinned values.