#set document(title: "12.1 Critical Values for t-Interval", author: "Kathryn Kozak")
#set page(width: 8.5in, height: auto, margin: 1in)
#import "@preview/cetz:0.5.2"
#set text(font: ("STIX Two Text", "Libertinus Serif", "New Computer Modern"), size: 10.5pt, lang: "en")
#show math.equation: set text(font: ("STIX Two Math", "New Computer Modern Math"))
#set par(justify: true, leading: 0.62em, spacing: 0.9em)
#set enum(spacing: 1.1em)   // room between list items so tall inline fractions don't collide
#set list(spacing: 1.1em)
#set table(stroke: 0.5pt + rgb("#c7ccd3"))

#let BLUE = rgb("#183B6F")     // brand navy — section bars + example/solution labels (white on navy 11.09:1)
#let ORANGE = rgb("#A94509")   // brand primary-700 — AA-safe deep orange for TEXT (5.93:1 on white; raw brand #F37021 is 2.94:1 and must never carry text)
#let RED = rgb("#DC2626")      // brand error-600
#let GREEN = rgb("#059669")    // brand success-600 (decoration only; small green text uses green-text #007942)

#show heading.where(level: 1): it => block(width: 100%, above: 0pt, below: 16pt,
  fill: gradient.linear(BLUE, rgb("#2C5AA0")), inset: (x: 14pt, y: 12pt), radius: 3pt,
  text(fill: white, weight: "bold", size: 19pt, it.body))
#show heading.where(level: 2): it => block(width: 100%, above: 18pt, below: 10pt,
  fill: BLUE, inset: (x: 10pt, y: 6pt), radius: 2pt,
  text(fill: white, weight: "bold", size: 12pt, it.body))
#show heading.where(level: 3): it => text(fill: ORANGE, weight: "bold", size: 12.5pt, it.body)
#show heading.where(level: 4): it => text(fill: BLUE, weight: "bold", size: 10.5pt, it.body)

#let examplebox(label, title, body) = block(width: 100%, breakable: true,
  fill: rgb("#EFF1F5"), stroke: 0.5pt + rgb("#CFDDF0"), radius: 4pt, inset: 10pt,
  above: 12pt, below: 12pt)[
  #block(below: 6pt)[#box(fill: BLUE, inset: (x: 6pt, y: 2pt), radius: 2pt,
    text(fill: white, weight: "bold", size: 8.5pt, label)) #h(0.4em) #strong[#title]]
  #body]

// rail = decorative left rule (raw brand token); labelcolor = AA-safe label text shade
#let notebox(label, rail, labelcolor, tint, body) = block(width: 100%, breakable: true, fill: tint,
    stroke: (left: 3pt + rail), inset: (left: 10pt, rest: 8pt), radius: (right: 4pt),
    above: 11pt, below: 11pt)[
    #text(fill: labelcolor, weight: "bold", size: 7.5pt, tracking: 0.5pt)[#upper(label)]
    #linebreak() #body]

#let solutionbox(body) = block(above: 4pt, below: 8pt)[
  #text(fill: BLUE, weight: "bold", size: 8.5pt)[Solution] #linebreak() #body]

#let figph(msg) = block(width: 100%, height: 60pt, fill: rgb("#f6f7f9"),
  stroke: (paint: rgb("#c7ccd3"), dash: "dashed"), radius: 4pt, inset: 10pt)[
  #align(center + horizon, text(fill: rgb("#889"), style: "italic", size: 9pt, msg))]

// Standardize inlined figure sizes: measure the natural CeTZ canvas, then scale to a
// consistent envelope (aspect-aware; see build_typst.py FIG_* constants). Unlike the
// print preamble, dimensions are FLOORED: in an editor a user can trim a figure to a
// degenerate 1-D shape (a bare line), and w/h or tw/w would then divide by zero.
#let _STD_W = 3.5
#let _WIDE_W = 5.6
#let _MAX_H = 3.4
#let _ASPECT_WIDE = 2.2
#let _UPSCALE_MAX = 1.15
#let stdfig(body) = context {
  let m = measure(body)
  let w = calc.max(m.width / 1in, 0.01)
  let h = calc.max(m.height / 1in, 0.01)
  let tw = if w / h > _ASPECT_WIDE { _WIDE_W } else { _STD_W }
  let s = calc.min(tw / w, _MAX_H / h, _UPSCALE_MAX)
  align(center, box(scale(x: s * 100%, y: s * 100%, reflow: true, body)))
}

#show figure: set block(breakable: false)
#set figure(gap: 8pt)
#show figure.caption: set text(size: 8.5pt, fill: rgb("#555"))


    
== 12.1#h(0.6em)Critical Values for t-Interval


    #figure(table(
  columns: 6, align: left, inset: 6pt,
  table.header([Degrees of Freedom (#emph[df])], [80%], [90%], [95%], [98%], [99%]),
  [1], [3.078], [6.314], [12.706], [31.821], [63.657],
  [2], [1.886], [2.920], [4.303], [6.965], [9.925],
  [3], [1.638], [2.353], [3.182], [4.541], [5.841],
  [4], [1.533], [2.132], [2.776], [3.747], [4.604],
  [5], [1.476], [2.015], [2.571], [3.365], [4.032],
  [6], [1.440], [1.943], [2.447], [3.143], [3.707],
  [7], [1.415], [1.895], [2.365], [2.998], [3.499],
  [8], [1.397], [1.860], [2.306], [2.896], [3.355],
  [9], [1.383], [1.833], [2.262], [2.821], [3.250],
  [10], [1.372], [1.812], [2.228], [2.764], [3.169],
  [11], [1.363], [1.796], [2.201], [2.718], [3.106],
  [12], [1.356], [1.782], [2.179], [2.681], [3.055],
  [13], [1.350], [1.771], [2.160], [2.650], [3.012],
  [14], [1.345], [.1761], [2.145], [2.624], [2.977],
  [15], [1.341], [1.753], [2.131], [2.602], [2.947],
  [16], [1.337], [1.746], [2.120], [2.583], [2.921],
  [17], [1.333], [1.740], [2.110], [2.567], [2.898],
  [18], [1.330], [1.734], [2.101], [2.552], [2.878],
  [19], [1.328], [1.729], [2.093], [2.539], [2.861],
  [20], [1.325], [1.725], [2.086], [2.528], [2.845],
  [21], [1.323], [1.721], [2.080], [2.518], [2.831],
  [22], [1.321], [1.717], [2.074], [2.508], [2.819],
  [23], [1.319], [1.714], [2.069], [2.500], [2.807],
  [24], [1.318], [1.711], [2.064], [2.492], [2.797],
  [25], [1.316], [1.708], [2.060], [2.485], [2.787],
  [26], [1.315], [1.706], [2.056], [2.479], [2.779],
  [27], [1.314], [1.703], [2.052], [2.473], [2.771],
  [28], [1.313], [1.701], [2.048], [2.467], [2.763],
  [29], [1.311], [1.699], [2.045], [2.462], [2.756],
  [30], [1.310], [1.697], [2.042], [2.457], [2.750],
  [31], [1.309], [1.696], [2.040], [2.453], [2.744],
  [32], [1.309], [1.694], [2.037], [2.449], [2.738],
  [33], [1.308], [1.692], [2.035], [2.445], [2.733],
  [34], [1.307], [1.691], [2.032], [2.441], [2.728],
  [35], [1.306], [1.690], [2.030], [2.438], [2.724],
  [36], [1.306], [1.688], [2.028], [2.434], [2.719],
  [37], [1.305], [1.687], [2.026], [2.431], [2.715],
  [38], [1.304], [1.686], [2.024], [2.429], [2.712],
  [39], [1.304], [1.685], [2.023], [2.426], [2.712],
  [40], [1.303], [1.684], [2.021], [2.423], [2.704],
  [41], [1.303], [1.683], [2.020], [2.421], [2.701],
  [42], [1.302], [1.682], [2.018], [2.418], [2.698],
  [43], [1.302], [1.681], [2.017], [2.416], [2.695],
  [44], [1.301], [1.680], [2.015], [2.414], [2.692],
  [45], [1.301], [1.679], [2.014], [2.412], [2.690],
  [46], [1.300], [1.679], [2.013], [2.410], [2.687],
  [47], [1.300], [1.678], [2.012], [2.408], [2.685],
  [48], [1.299], [1.677], [2.011], [2.407], [2.682],
  [49], [1.299], [1.677], [2.010], [2.405], [2.680],
  [50], [1.299], [1.676], [2.009], [2.403], [2.678],
  [51], [1.298], [1.675], [2.008], [2.402], [2.676],
  [52], [1.298], [1.675], [2.007], [2.400], [2.674],
  [53], [1.298], [1.674], [2.006], [2.399], [2.672],
  [54], [1.297], [1.674], [2.005], [2.397], [2.670],
  [55], [1.297], [1.673], [2.004], [2.396], [2.668],
  [56], [1.297], [1.673], [2.003], [2.395], [2.667],
  [57], [1.297], [1.672], [2.002], [2.394], [2.665],
  [58], [1.296], [1.672], [2.002], [2.392], [2.663],
  [59], [1.296], [1.671], [2.001], [2.391], [2.662],
  [60], [1.296], [1.671], [2.000], [2.390], [2.660],
  [61], [1.296], [1.670], [2.000], [2.389], [2.659],
  [62], [1.295], [1.670], [1.999], [2.388], [2.657],
  [63], [1.295], [1.669], [1.998], [2.387], [2.656],
  [64], [1.295], [1.669], [1.998], [2.386], [2.655],
  [65], [1.295], [1.669], [1.997], [2.385], [2.654],
  [66], [1.295], [1.668], [1.997], [2.384], [2.652],
  [67], [1.294], [1.668], [1.996], [2.383], [2.651],
  [68], [1.294], [1.668], [1.995], [2.382], [2.650],
  [69], [1.294], [1.667], [1.995], [2.382], [2.649],
  [70], [1.294], [1.667], [1.994], [2.381], [2.648],
  [71], [1.294], [1.667], [1.994], [2.380], [2.647],
  [72], [1.293], [1.666], [1.993], [2.379], [2.646],
  [73], [1.293], [1.666], [1.993], [2.379], [2.645],
  [74], [1.293], [1.666], [1.993], [2.378], [2.644],
  [75], [1.293], [1.665], [1.992], [2.377], [2.643],
  [76], [1.293], [1.665], [1.992], [2.376], [2.642],
  [77], [1.293], [1.665], [1.991], [2.376], [2.641],
  [78], [1.292], [1.665], [1.991], [2.375], [2.640],
  [79], [1.292], [1.664], [1.990], [2.374], [2.640],
  [80], [1.292], [1.664], [1.990], [2.374], [2.639],
  [81], [1.292], [1.664], [1.990], [2.373], [2.638],
  [82], [1.292], [1.664], [1.989], [2.373], [2.637],
  [83], [1.292], [1.663], [1.989], [2.372], [2.636],
  [84], [1.292], [1.663], [1.989], [2.372], [2.636],
  [85], [1.292], [1.663], [1.988], [2.371], [2.635],
  [86], [1.291], [1.663], [1.988], [2.370], [2.634],
  [87], [1.291], [1.663], [1.988], [2.370], [2.634],
  [88], [1.291], [1.662], [1.987], [2.369], [2.633],
  [89], [1.291], [1.662], [1.987], [2.369], [2.632],
  [90], [1.291], [1.662], [1.987], [2.368], [2.632],
  [91], [1.291], [1.662], [1.986], [2.368], [2.631],
  [92], [1.291], [1.662], [1.986], [2.368], [2.630],
  [93], [1.291], [1.661], [1.986], [2.367], [2.630],
  [94], [1.291], [1.661], [1.986], [2.367], [2.629],
  [95], [1.291], [1.661], [1.985], [2.366], [2.629],
  [96], [1.290], [1.661], [1.985], [2.366], [2.628],
  [97], [1.290], [1.661], [1.985], [2.365], [2.627],
  [98], [1.290], [1.661], [1.984], [2.365], [2.627],
  [99], [1.290], [1.660], [1.984], [2.365], [2.626],
  [100], [1.290], [1.660], [1.984], [2.364], [2.626],
  [101], [1.290], [1.660], [1.984], [2.364], [2.625],
  [102], [1.290], [1.660], [1.983], [2.363], [2.625],
  [103], [1.290], [1.660], [1.983], [2.363], [2.624],
  [104], [1.290], [1.660], [1.983], [2.363], [2.624],
  [105], [1.290], [1.659], [1.983], [2.362], [2.623],
))