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SRM602 Formulas – Numbers/Letters on the left correspond to TI-83plus STAT List

General Notes:

Reject H_o if actual test value (t, z, chi, F) < critical value or p value < alpha value

o P is the probability that the sample value is based on chance if the null is true

§ Reject if p is low because the value of chance is small

§ Accept if p is high, represents the population

§ 0 ≤ p ≤ 1

1: Z-Test... Test for 1 µ, known σ;

H_o: µ = [specific number] α₂; H_o: µ < or > [specific number] α₁

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2: T-Test... Test for 1 µ, unknown σ; H_o: µ = µ_o α₂; H_o: µ < or > µ_o α₁

= ; df = (n-1) ; observed effect =

4: 2-SampTTest... Test comparing 2 µ’s, unknown σ’s;

H_o: µ₁ = µ₂ α₂; H_a: u₁-u₂ > 0 & H_a: u₁-u₂ > 0 α₁; H_a: µ₁ ≠ µ₂ α₂

Sample Sizes Unequal and Variances Unequal – Not Pooled

; ;( when n₁ & n₂ >= 5) df (v) = ; ;

Independent Samples – Treat1 vs. Treat2 same size/equal variance – Pooled

; ; ;

df =

Paired Observations – Single t-test on Differences

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df = (n-1) where n is the number of pairs;

H_o: µ_diff = 0 α₂; H_a: µ_diff < or > 0 α₁ ; H_a: µ_diff ≠ 0 α₂

5: 1-PropZTest... Test for 1 proportion; (used for categorical data)

H_o: π = π_o (π_o = given value to test) α₂; H_a: π < or > π_o α₁ H_a: π ≠ π_o α₂

π (population proportion of successes) =

p (sample proportion of successes) =

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Standard deviation of a dichotomous variable

Variance of proportion ;

Significance Test for π: z = This is valid when both expected counts — expected successes nπ₀ and expected failures n(1 − π₀) — are each 10 or larger.

7: ZInterval... Confidence interval for 1 µ, known σ

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; z^*=Critical Value; ; S.E. =

8: TInterval... Confidence interval for 1 µ, unknown σ

t^*=Critical Value; df = (n-1);

0: 2-SampTInt... Confidence interval for difference of 2 µ’s, unknown σ’s

; df = ; ;

A: 1-PropZInt... Confidence interval for 1 proportion:

Usually for H_o: π = π_o α₂; H_a: π < or > π_o α₁ ; H_a: π ≠ π_o α₂

p (sample proportion of successes) = ; q=(1-p)

Confidence Interval for π

; ; z^* = critical value

Or

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(method II is less accurate)

C: 2-Test... Chi-square test for 2-way tables: α₁ only;

H_o:There is no relation between factor A and factor B; df = (# of rows - 1)(# of cols - 1)

(Done for each table cell)

D: 2-SampϜTest... Test comparing 2 σ’s: (calculator does only 2 σ’s)

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H_o: All µ’s are equal & H_a: Not all µ’s equal ; α₁

F =

df = (I – 1)/(N-I); where I = number of levels & N = total number of observations

E: LinRegTTest... t test for regression slope and p – Used to assess whether the observed relationship is statistically significant (not entirely explained by chance events due to random sampling).

H_o: β = 0 α₂; hypothesis of no correlation between x and y in the population from which data was drawn.

H_a: β≠0 α_2; ; < 0 or > 0 α₁

; Where α is the y-intercept and β is slope or rate of change

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; Slope: ; where r is the correlation coefficient

= Root MSE on SAS

β Confidence Interval = ; ; df = n-2; t^*=Critical Value (CI by hand)

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Level C prediction for a single observation – Use x to predict y

; ; df = (n-2); x^* is x value to predict y (by hand)

F: ANOVA One-way analysis of variance

: MISC Formulas

Variance:

;

Goodness of Fit – (Often looks like a chi- table with 1 row): α₁ only; H_o: p = p_i

Expected count = np_i; n = row(table) total; p_i = given percent/fraction for each cell or 1/number of cells; df = (k-1) where k = # of cells

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Slope: ; where r is the correlation coefficient

Error Notes

	Null True	Null False
Reject Ho	Type 1 error (false positive or false rejection) Mediate by changing alpha Alpha = probability of Type 1 error	NO Error
Fail to Reject	NO Error	Type ll Error (false negative or false acceptance) Beta Power = (1-Beta) Mediate – increase sample size Decrease variability Increase alpha

Correct Interval wording