Inferential Statistics: Basic Cases / MATH200 (TC3, Brown)

Summary: This table organizes procedures for basic inferential statistics into a chart of Cases. You may use this page on quizzes beginning with Chapter 9 and on the final exam.

Case Number and Description		Pop. Param.	TI-83/84/89 Procedures
NUMERIC DATA SRS required: n ≥ 30, or sample is normal with no outliers
0	One pop. mean, known σ	μ	CI: `ZInterval`; HT: `Z-Test`; sample size: MATH200A part 5
1	One pop. mean, unknown σ	μ	CI: `TInterval`; HT: `T-Test`; sample size (optional): MATH200A part 5
3	Mean difference for paired data	μ_d	CI: `TInterval`; HT: `T-Test`; (optional) List Operations for Paired t Test on TI-83/84
4	Difference of 2 indep. pop. means, unpaired data	μ₁, μ₂ μ₁−μ₂	CI: `2-SampTInt`; HT: `2-SampTTest`; requirements apply to each sample
9	Linear correlation coefficient	ρ or r	CI: n/a; HT: Decision Points for Correlation Coefficient
BINOMIAL DATA
2	One pop. proportion	p	CI: `1-PropZInt`; HT: `1-PropZTest` (small sample HT: MATH200A part 3 or `binomcdf`); sample size: MATH200A part 5
2	One pop. proportion	HT requires SRS, 20n ≤ N, and n p_o (1−p_o) ≥ 10 CI requires SRS, 20n ≤ N, and n p̂ (1−p̂) ≥ 10
5	Difference of 2 pop. proportions	p₁, p₂ p₁−p₂	CI: `2-PropZInt`; HT: `2-PropZTest`; sample size: MATH200A part 5
5	Difference of 2 pop. proportions	HT requires SRS, 20n₁ ≤ N₁, 20n₂ ≤ N₂, and (n₁+n₂) p̂ (1−p̂) ≥ 10 CI: SRS, 20n₁ ≤ N₁, 20n₂ ≤ N₂, n₁ p̂₁ (1−p̂₁) ≥ 10, and n₂ p̂₂ (1−p̂₂) ≥ 10
CATEGORICAL DATA SRS required: (a) every E≥5 or (b) no E<1 and no more than 20% of cells have E<5
6	Goodness of fit (GOF) or multinomial	none	CI: undefined; HT: MATH200A part 6 (TI-89: `Chi2 GOF` or Testing Goodness of Fit on TI-89)
7	Independence or homogeneity (in contingency table)	none	CI: undefined; HT: `χ²-Test` or MATH200A part 7 (TI-89: `Chi2 2-way`)

Acknowledgement: This table was inspired by Dabes & Janik’s Statistics Manual (1999) page 163; I have modified the format substantially.