Casio FX-9750G, FX-9860GII IConfidence Interval, IDistribution (Continuous), p, p(x)dx, Left, Right = o, Left, Right = (o1 – o2), Left, Right = (o1 – o2), Left, Right = x/n + Z( /2)

IConfidence Interval

Left: confidence interval lower limit (left edge)

Confidence Interval

Right: confidence interval upper limit (right edge)

1-Sample Z Interval	 					α
			= o + ( /2) · /'
								α		2	2
2-Sample Z Interval	 		= (o1 – o2) + (						/2)	 /1 +  /2
										1	2
1-Prop Z Interval						α			1/n · (x/n · (1 – x/n))
	Left, Right = x/n + Z( /2)
2-Prop Z Interval	Left, Right = (x1/n1 – x2/n2)
		α
	+	Z( /2)	(x1/n1 · (1 – x1/n1))/n1							+ (x2/n2 · (1 – x2/n2))/n2
1-Sample t Interval	Left, Right = o			+	tn−1(α /2) · sx/'n
2-Sample t Interval	Left, Right = (o1 – o2)						+	tn1+n2−2 (α /2)			sp2(1/n1 + 1/n2)
(pooled)	sp = ((n1 – 1)sx12 + (n2 – 1)sx22)/(n1 + n2 – 2)
2-Sample t Interval	Left, Right = (o1 – o2)						+	tdf (α /2)		sx12/n1 + sx22/n2
	df = 1/(C2/(n1 – 1) + (1 – C)2/(n2 – 1))
(not pooled)
	C = (sx12/n1)/(sx12/n1 + sx22/n2)

Α: level of significance Α = 1 − [C-Level ] C-Level : confidence level (0  C-Level 1)

Z(Α/2): upper Α/2 point of standard normal distribution

tdf (Α/2): upper Α/2 point of t distribution with df degrees of freedom

IDistribution (Continuous)

Distribution

Probability Density

Cumulative Distribution

Normal

p(x) = 1

e–

(x –  )2

2 2



Distribution

(

> 0)

2 

–

df+1

df + 1

1 +

x

2

2

Student-t



2

df

Distribution

p(x) =

df

 df



2

p =

Upper

df

df

x

p(x)dx

p(x) =

1

1

2

x

–1 e–

Lower

Χ2 Distribution

2

2

df

2



(x 0)

2

 ndf + ddf

ndf ndf

–1

– ndf + ddf

p(x) =

2

ndf

2

x 2

ndf

x

2

1 +

ndf

ddf

ddf

F Distribution



 

ddf

2

2

(x 0)

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