7.5.1: Project Check-In 4
- Page ID
- 60442
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Project Check-In 4: Comparing Means with Confidence Intervals
You've now learned how to build a confidence interval for a sample mean — and in your housing affordability project, that opens up exciting possibilities for comparison!
TODO: Use your collected housing data to construct confidence intervals for the mean price in at least two different cities (or ZIP codes/regions) within your dataset. Then, place them side by side in a graph. You'll reflect both on the technical results and the story they tell.
What to Include:
- Construct at least two confidence intervals for average housing prices — each one based on a different group (e.g., city or ZIP code).
- Each confidence interval should include:
- The sample mean
- The sample size (n)
- The sample standard deviation (s)
- The margin of error and the level of confidence used (use 95% unless you have a reason to choose differently)
- The resulting confidence interval: (lower bound, upper bound)
- Graph your confidence intervals on a number line or bar chart:
- You can draw this by hand, or use Google Sheets, Excel, Desmos, or another tool
- Label each interval clearly with its city or region
- Make sure the graph's axis is scaled to allow visual comparison
Reflection Questions:
- Which group/region had the highest estimated mean housing price? Which one had the lowest?
- Do any of your confidence intervals overlap? What might that suggest?
- Is the difference between regions statistically significant? Why or why not?
- What could affect the precision of your intervals (i.e., what makes them wider or narrower)?
- How might sampling bias, variation, or small sample size impact your conclusions?
Visualization Example (Optional):
Midtown (95% CI): ───────────────
West Side (95% CI): ────────
Suburbs (95% CI): ──────────────────────
Tip: Align your intervals along a shared price scale so they're easy to interpret together.
Your Submission Should Contain:
- A short paragraph restating your question and what you set out to compare
- Each confidence interval and how it was calculated (with formulas and/or tech screenshots)
- A clearly labeled graph showing multiple confidence intervals
- Answers to the reflection questions above
- Any notes about limitations or interesting discoveries from your dataset
Helpful Tip: You can revisit the worked examples in Chapter 7.4 for step-by-step guidance on calculating confidence intervals using summary statistics. Copy a template, then adjust for each region.