CONFIDENCE INTERVAL FORMULAE STAT 512, J. TEBBS
•Exact confidence interval for a normal mean µwhen σ2=σ2
0is known:
Y±zα/2σ0
√n
•Large-sample confidence interval for a population mean µ:
Y±zα/2S
√n
•Large-sample confidence interval for a population proportion p:
bp±zα/2rbp(1 −bp)
n
•Large-sample confidence interval for the difference of two population
means µ1−µ2:
(Y1+ −Y2+)±zα/2sS2
1
n1
+S2
2
n2
•Large-sample confidence interval for the difference of two population
proportions p1−p2:
(bp1−bp2)±zα/2sbp1(1 −bp1)
n1
+bp2(1 −bp2)
n2
•Small-sample confidence interval for a normal mean µ:
Y±tn−1,α/2S
√n
•Small-sample confidence interval for the difference of two normal means
µ1−µ2when σ2
1=σ2
2(equal population variances):
(Y1+ −Y2+)±tn1+n2−2,α/2Spr1
n1
+1
n2
S2
p=(n1−1)S2
1+ (n2−1)S2
2
n1+n2−2
•Small-sample approximate confidence interval for the difference of two
normal means µ1−µ2when σ2
16=σ2
2(unequal population variances):
(Y1+ −Y2+)±tν,α/2sS2
1
n1
+S2
2
n2
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