Inferential Statistics Cases

Summary: This table organizes procedures for inferential statistics into a chart of Cases. (The Case numbers are useful for reference, although they are not standard statistics terminology.) The ones marked with ★ are covered in the textbook, and most of the rest are covered in separate optional Web pages. All links are live in the online version of this page.

Case Number and Description		Pop. Param.	TI-83/84/89 Procedures (CI=conf int, HT=hypothesis test, SS=sample size) All require random sample or randomization, and 10n ≤ N; additional requirements are noted in each case.
NUMERIC DATA
0	One pop. mean, known σ (Do you really know σ?)	μ	Required: n ≥ about 30 or normal with no outliers. CI: `ZInterval`; HT: `Z-Test` SS: MATH200A part 5
1★	One pop. mean, unknown σ	μ	Required: n ≥ about 30 or normal with no outliers. CI: `TInterval`; HT: `T-Test` SS: MATH200A part 5
1S	One pop. standard dev.	σ	Population must be ND, not just roughly normal. CI and HT: MATH200B part 5 (not TI-89)
3★	Mean difference for paired data	μ_d	Required: n ≥ about 30, or differences are normal with no outliers. CI: `TInterval` using the differences; HT: `T-Test` using the differences
4★	Difference of 2 indep. pop. means, unpaired data	μ₁, μ₂ or μ₁−μ₂	Required: in each sample, n ≥ about 30 or normal with no outliers. CI: `2-SampTInt`; HT: `2-SampTTest`
4S	Two pop. standard dev.	σ₁/σ₂	Both populations must be ND, not just roughly normal. CI: n/a; HT: `2-SampFTest`
8	Equality of several pop means	μ₁, μ₂, μ₃, ...	CI: n/a; HT: `ANOVA`; see One-Way ANOVA for procedure and requirements.
9	Linear correlation coefficient	ρ or r	Required: for any given x, population of y is ND. CI and HT: MATH200B part 6 TI 89 HT: `LinRegTTest`
10B	Slope of regression line	β₁	Required: residuals are ND. CI and HT: MATH200B part 7 TI-89 CI: `LinRegTInt`; TI-89 HT: `LinRegTTest`
10Y	Predicted values of y	μ_{y\|x_j}, y_j	Required: residuals are ND. MATH200B part 7 (not TI-89)
YES/NO COUNTS — INFERENCES ABOUT PROPORTIONS
2★	One pop. proportion	p	CI: `1-PropZInt`; requires ≥ 10 successes and ≥ 10 failures in sample. HT: `1-PropZTest`; requires expected successes np_o ≥ 10 and expected failures n−np_o ≥ 10. HT w/ small samples: MATH200A part 3 or `binomcdf` SS: MATH200A part 5
5★	Difference of 2 pop. proportions	p₁, p₂ p₁−p₂	CI: `2-PropZInt`; each sample requires ≥ 10 successes and ≥ 10 failures. HT: `2-PropZTest`; requires same as CI. If that’s not met, use pooled p̂ to test that n₁p̂, n₁−n₁p̂, n₂p̂, n₂−n₂p̂ are all ≥ 10. SS: MATH200A part 5
CATEGORY COUNTS — INFERENCES ABOUT MODELS
6★	Goodness of fit (GOF) or multinomial	none	CI: undefined; HT: MATH200A part 6 TI-89 HT: `Chi2 GOF` or How to Test Goodness of Fit on TI-89 Required: every expected value ≥ about 5.
7★	Independence or homogeneity (in 2-way table)	none	CI: undefined; HT: `χ²-Test` or MATH200A part 7 TI-89 HT: `Chi2 2-way` Required: every expected value ≥ about 5.