Math 116
Inference formulas
[normal-ditribution-based methods]
[All involve assumptions that:
1. Sample is random sample
2. Population much larger than sample
3. For means: variable is approximately normal (mounded up in middle) in population or sample large (n>30)
4. For proportion: sample large enough [number of successes, number of failures both at least 10)]
"Sample statistic" is the statistic used to estimate the parameter, SE is the standard error (= standard deviation) of that statistic
(thus is the standard deviation of - which varies between samples (not within one sample) etc.)
For estimation (confidence intervals): sample value ± E , with E = (t* or Z*)SE
For tests test statstic is sample t (or sample Z) =
In stating the alternative hypothesis HA , the "R" can be ">" or "<" or "≠"
p-value
For ">" p-value is P(random t > sample t) -read from t-table
For "<" p-value is P(random t < sample t) - read t-table as if all t's are negative
For "≠" p-value is P(random t > )-ignore sign of sample t, double the table p-value
[Same for Z - but df = ∞]
Parameter / sample value / SE / Error bound / interval / hypotheses / test statistic
Mean m / x / s/ / t*s/ / x± t*s/ / H0: m = K
HA: m R K
/ sample t =
proportion p / z* / ± z* / H0: p = K
HA: p R K
/ sample z =
difference of means
m1 - m2 / x1-x2 / t* / x1-x2 ± t* / H0: m1 = m2
HA: m1 R m2 / sample t =
mean of a difference (matched pairs)
mD / D / sD/ / t*sD/ / D / H0: mD = 0
HA: mD R 0 / sample t =