TC3 → Stan Brown → Statistics → Inferential Cases (Basic)
revised 29 Oct 2013

# Inferential Statistics: Basic Cases

Summary: This table organizes procedures for basic inferential statistics into a chart of Cases. (The Case numbers are useful for reference, although they are not standard statistics terminology.) You may use this page on quizzes beginning with Chapter 9 and on the final exam. All links are live in the online version of this page.

Caution: All cases require random sample or randomization, and n ≤ about 10% of N (or 10n ≤ N). See the table for additional requirements for specific cases.

See also: While you’re getting used to the cases, practice with the interactive Triage: Which Inferential Stats Case Should I Use?. For more cases see Inferential Statistics Cases.

Case Number
and Description
Pop.
Param.
TI-83/84/89 Procedures
(CI=conf int, HT=hypothesis test, SS=sample size)
NUMERIC DATA
required: n ≥ about 30 or normal with no outliers
1One pop. mean, unknown σ μ CI: `TInterval`; HT: `T-Test`
SS: MATH200A part 5
3Mean difference for paired data μd Requirements apply to the differences.
CI: `TInterval`; HT: `T-Test`
4Difference of 2 indep. pop. means, unpaired data μ1, μ2
μ1−μ2
Requirements apply to each sample.
CI: `2-SampTInt`; HT: `2-SampTTest`
9Linear correlation coefficient ρ or r CI: n/a; HT: Decision Points for Correlation Coefficient
BINOMIAL DATA
2One pop. proportion p CI requires ≥ 10 successes and ≥ 10 failures in sample
CI: `1-PropZInt`
HT requires expected successes npo ≥ 10 and failures nnpo ≥ 10
HT: `1-PropZTest`
HT w/ small samples: MATH200A part 3 or `binomcdf`
SS: MATH200A part 5
5Difference of 2 pop. proportions p1, p2
p1p2
CI requires ≥ 10 successes and ≥ 10 failures in each sample
CI: `2-PropZInt`
HT: `2-PropZTest`
HT requires ≥ 10 successes and ≥ 10 failures in each sample, or n1, n1n1, n2, n2n2 all ≥ 10 using pooled
SS: MATH200A part 5
CATEGORICAL DATA
required: all expected values ≥ about 5
6Goodness of fit (GOF) or multinomial none CI: undefined; HT: MATH200A part 6
TI-89 HT: `Chi2 GOF` or Testing Goodness of Fit on TI-89
7Independence or homogeneity
(in 2-way table)
none CI: undefined; HT: `χ²-Test` or MATH200A part 7
TI-89 HT: `Chi2 2-way`

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

## What’s New

• 29 Oct 2013: Move Case 2 requirememnts for HT before the HT itself.
• 24 Aug 2013: In one-proportion HT, identify requirement as expected successes and failures.
• 30 Jul 2013:
• 23 Jun 2013:
• Clarify requirements.
• Lose Case 0 (one population mean, known σ), because it’s just not realistic.
• Rearrange text in the table and clean up formatting for easier use.
• (intervening changes suppressed)
• 26 Dec 2009: Create this separate Basic Cases document for just the ones required in class; add Requirements to the three data types.
• (intervening changes suppressed)
• 10 Nov 2007: new document, inspired by Dabes & Janik’s Statistics Manual (1999)

This page is used in instruction at Tompkins Cortland Community College in Dryden, New York; it’s not an official statement of the College. Please visit www.tc3.edu/instruct/sbrown/ to report errors or ask to copy it.

For updates and new info, go to http://www.tc3.edu/instruct/sbrown/stat/