Chapter 9: Hypothesis - Step 1: Hypotheses H₀: µ = µ₀ VS Hₐ: µ ≠ µ₀

- Step 2: AssumptionsVariable is quantitative/categoricalData obtained randomized?Population distribution approximately normal (SIZE)?

- Step 3: Compute test statisticFor Population Proportion:

Z=p−p0

√ p0q0n , p is stat, p0 is pop

For Population Mean

t=x−µ0s

√n , df = n – 1

- Step 4: Derive p-value

- Step 5: ConclusionSmall p, reject H₀ and conclude that…Large p, evidence to support H₀

Chapter 10: 2 Populations

CI for difference of Means (Independent samples)

(x1−x2 )±t a2

.√( s12

n1 )+(s22

n2)

CI for difference of 2 proportions

( p1−p2)±Z a2

.√( p1q1n1 )+( p2q2n2 )Test stat for difference of Means

(Independent samples)

t=(x1−x2)−(µ1−µ2 )

√( s12

n1 )+(s22

n2)

Test stat: diff of means (dependent)

t=d−µdSd/√n

Test stat for diff of 2 proportions

Z=p1−p2

√ pq( 1n1 + 1n2 ), pop . pknown

else, use pooled p

Chapter 13: Regression Analysis

r-coefficient / Regression:

r= 1n−1∑ ( x− x

Sx¿)(y− yS y

)¿

sum of squares = ∑ (residuals)2

= ∑ ( y− y)2

standardized residual = ( y− y)se ( y− y)

slope: b=r (SxS y

)

Regression AnalysisAssumptions:

- Linear, as from scatter plot- Data obtained randomly- Points have similar spread at

different values of x

Test stat: t=b−0se

CI: b± t a/2 ( se ) , df=n−2Residual

s.d: s=√∑ ( y− y )2

n−2CI:

µ= y ± ta /2 .(se of y )

PI: y ±2 s