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TI-84+ Quick Reference Sheet — AP Statistics

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Calculator ID #

Choose 2nd → MEM → #1 About
ID: ***** ***** *****

Been Playing Games?

Run DEFAULTS to reset calculator.
2nd MEM → #7 Reset → #2 Defaults → #2 Reset

To Get Statistical Information
  1. Place data in Lists: STAT → EDIT
  2. Engage 1-Variable Statistics: STAT → CALC → #1 1-VAR STATS
  3. On Home Screen indicate list: 1-VAR STATS L₁

\( \bar{x} = \text{mean} \), \( s_x = \text{sample SD} \), \( σ_x = \text{population SD} \)
\( Q_1 = \text{first quartile} \), \( \text{med} = \text{median} \), \( Q_3 = \text{third quartile} \)
\( n = \text{sample size} \)

To Plot Histograms & Box-Whisker Plots
  1. Place data in Lists: STAT → EDIT
  2. Set up plot info: STAT PLOT → #1 <ENTER>
    Highlight ON and choose symbol.
    XList: L₁, Freq: 1
  3. Graph: ZOOM #9 → TRACE
  4. Xscl in WINDOW controls bar width.
    Integer values are easiest to read.
Diagnostics ON

Must be ON to see correlation coefficient (r).

  • MODE → StatDiagnostics → ON
  • or CATALOG → ALPHA D → DiagnosticOn → ENTER → ENTER
To Get Scatter Plots & Regressions

(Linear, Quadratic, Exponential, Power, etc.)

  1. Enter data: STAT → EDIT
  2. Graph scatter plot: STAT PLOT → #1 → ENTER → choose ON
  3. Set XList = L₁, YList = L₂
  4. Graph: ZOOM #9
  5. Regression: STAT → CALC → #4 LinReg(ax+b)
  6. Show equation on graph:
    VARS → Y-VARS → FUNCTION → Y₁ or ALPHA F4
  7. Home screen: LinReg(ax+b) L₁, L₂, Y₁
To Get Residuals
  1. After regression, residuals auto-store in list RESID.
  2. Go to top of L₃ → 2nd STAT → #7 RESID → ENTER
  3. STAT PLOT → Plot1 → ON
  4. Type: Scatter | XList = L₁ | YList = L₃
  5. Graph: ZOOM #9 (ZoomStat)
Normal Distributions (2nd → VARS)
FunctionDescription
normalcdf(lower, upper, mean, s.d.)Finds cumulative probability (use 1099 for ∞)
normalpdf(x, mean, s.d.)Graphs the normal curve
ShadeNorm(lower, upper, mean, s.d.)Shows shaded area and % under curve
invNorm(%, mean, s.d.)Finds z-score for given percentile
Student-t Distributions (2nd → VARS)
  • tpdf(x, df): Probability density (graph only)
  • tcdf(lower, upper, df): Distribution probability
  • invT(left-tail area, df): Finds t-score (not on TI-83)
Binomial Distributions (2nd → VARS)
  • binompdf(n, p, r): Probability of exactly r successes
  • binomcdf(n, p, r): Probability of ≤ r successes (cumulative)
Geometric Distributions (2nd → VARS)
  • geometpdf(p, r): Probability of first success on r-th trial
  • geometcdf(p, r): Probability of success within r trials

Formula: \( P(X=r) = (1-p)^{r-1}p \)

Generating Random Numbers
  1. randInt(a,b): Random integer between a & b
  2. randInt(a,b,n): Generates n integers
  3. randInt(0,10,100) → L₁: Stores 100 integers in List 1
  4. randIntNoRep(a,b): No repeats
  5. rand: Random decimals (0–1)
  6. rand*12 → L₁: Random decimals scaled 0–12
  7. randNorm(mean, s.d., n): Generates random normal samples
  8. Re-seed: Type 5 → rand (sets new seed)
Math Formula

\( (1-p)^{r-1}p \)
p = prob. success
r = r-th trial

Source: TI-84+ Quick Reference Sheet (AP Statistics) — Recreated for students

TI-84+ Quick Reference Sheet — Inferential Testing, CI & ANOVA

Stat vs Data: given actual data choose Data • given summary statistics (mean, s.d.) choose Stats.

Inferential Testing — STAT (TESTS)

1. Z-Test( )
• Tests for one unknown population mean when population s.d. is known.
Use: (1) pop. s.d. is known, (2) sample mean is known, (3) don’t know pop. mean, (4) to test sample mean with some value.

2. T-Test( )
• Test for one unknown pop. mean when pop. s.d. unknown.
Use: (1) sample mean is known, (2) don’t know pop. mean, (3) to test sample mean with some value.

3. 2-Sample ZTest( )
• Test comparing two means when both pop. s.d. are known.
• It is unusual to know both pop. s.d.
• Draw shows z-score and p-value.

4. 2-Sample TTest( )
• Test comparing two means when both pop. s.d. are unknown.
Use: (1) Both sample means and s.d. are known, (2) don’t know pop. means, (3) to test sample mean with some value.

5. 1-Prop ZTest( )
• Tests null hypothesis (no. of successes x, sample size n, alt. hypothesis, display option).
• Computes a test for one proportion of successes.
• Calculates z-score, p-value, and proportion for sample population.
• If given p-hat instead of # of successes x, calculate x by multiplying p-hat × n and rounding to nearest integer.

6. 2-Prop ZTest( )
• Test comparing two proportions of successes.
Use: (1) Working with 2 populations with different n values where both proportions of success are known, (2) to test if there is a statistical difference.

7. Chi-Square Test( )
• Assesses goodness of fit between observed values and those expected.
• Requires observed and expected data in matrix form.
• χ²-Test (matrix observed data, matrix expected data, display option).

8. Chi-Square GOF Test (Goodness of Fit)
• χ² GOF-Test (works with lists).
• Use for simple random sampling, 1 categorical variable, and expected frequency of at least 5.

Using Test Editors
  1. Select Data or Stats input:
    • Select Data to enter data lists.
    • Select Stats to enter statistics (mean, s.d., number).
  2. Enter values for arguments:
    • μ₀ = hypothesized value of population mean being tested
    • σ = known pop. s.d. (> 0)
    • List = name of list containing data
    • Freq = name of list containing frequency (defaults to 1)
  3. Select alternative hypothesis:
    • 1st option for Z-Test
    • 2nd for 2-SampTTest
    • 3rd for 2-PropZTest
  4. Select Calculate or Draw:
    • Calculate → shows test calculations on home screen (used for Confidence Intervals).
    • Draw → shows a graph (auto-adjusted window).
Confidence Intervals (CI) — STAT (TESTS)

Calculates confidence interval for an unknown mean or proportion of successes.

1. ZInterval( )
• Computes CI for unknown pop. mean when known s.d.
• Use when sample mean and s.d. are known.
• Assume population distribution is normal.

2. TInterval( )
• Computes CI for unknown pop. mean with unknown s.d.
• Use when sample mean and s.d. are known.
• Assume distribution is normal.

3. 2-SampZInt( )
• Computes CI for difference between 2 population means when s.d. are known (rare case).
• Depends on user-specified confidence level.

4. 2-SampTInt( )
• Computes CI for difference between 2 population means when both s.d. are unknown.
• Use when both sample means and s.d. are known.
• Assume both samples are normally distributed.
• Depends on user-specified confidence level.

5. 1-PropZInt( )
• Computes CI for unknown proportion of successes.
• Use when sample size and # of successes are known.
• Depends on user-specified confidence level.

6. 2-PropZInt( )
• Computes CI for difference between proportions of successes in 2 populations.
• Use when 2 samples have different # of successes.
• Depends on user-specified confidence level.

LinRegTTest — STAT (TESTS)
  • Computes linear regression on data and performs t-test on slope or correlation coefficient.
  • Residuals are created and stored in RESID.
  • Used to test the degree of relationship strength.

LinRegTInt:
Computes linear regression T confidence interval for slope coefficient \( b \).
If the confidence interval contains 0 → insufficient evidence that the data exhibits a linear relationship.

Chi-Square Distribution — DISTR (2nd VARS)

χ²pdf(x, df): Yields probability density function value — plots χ² curve with x as the variable.
The mean of a χ² distribution equals the number of degrees of freedom.

χ²cdf(lower bound, upper bound, df): Computes χ² distribution probability over interval.
Finds area under χ² curve between bounds (P[lower < X² < upper]).

ANOVA — STAT (TESTS)

One-way analysis of variance:
ANOVA(L₁, L₂, L₃, L₄)
• Compares the means of two to 20 populations.
• Determines if the means differ significantly.
• Computes F-ratio = variance between / variance within groups.
• SS = sum of squares, MS = mean squares.

Source: TI-84+ Quick Reference Sheet (AP Statistics) — Inferential Testing & Confidence Intervals

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