[SOLVED] STATS 101G/STATS 108

– 41 – STATS 101
STATS 101G
STATS 108
FORMULAE
Confidence intervals and t-tests
Confidence interval: estimate± t×se(estimate)

t-test statistic: t0 =

estimate− hypothesised value

standard error

Applications:

1. Single mean μ: estimate = x; df = n− 1

2. Single proportion p: estimate = p̂; df = ∞

3. Difference between two means μ1 − μ2: (independent samples)

estimate = x1 − x2; df = min(n1 − 1, n2 − 1)

4. Difference between two proportions p1 − p2:

estimate = p̂1 − p̂2; df = ∞

Situation (a): Proportions from two independent samples

Situation (b): One sample of size n, several response categories

Situation (c): One sample of size n, many yes/no items

The F -test (ANOVA)

F -test statistic: f0 =

s2B

s2W

; df1 = k − 1, df2 = ntot − k

The Chi-square test

Chi-square test statistic: χ2

0

=

∑

all cells in the table

(observed − expected)2

expected

Expected count in cell (i, j) =

RiCj

n

df = (I − 1)(J − 1)

Regression

Fitted least-squares regression line: ŷ = β̂0 + β̂1x

Inference about the intercept, β0, and the slope, β1: df = n− 2