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Chapter 10 « Estimation and Hypothesis Testing:
Two Populations
+ Mean of the sampling distribution of x, — x3:
Hs,-3, Hy Me
- Confidence interval for 4; — y for two independent
samples using the normal distribution when a and o, are
known:
where o, - [oi
nme Wy
(% — %) + 20,
nae
Ay
+ Test statistic for a test of hypothesis about yz, — fz for two
independent samples using the normal distribution when o,
and a2 are known:
- For two independent samples taken trom two populations
with equal but unknown standard deviations:
Pooled standard deviation:
jy — 1
5, =
’ n, +n,—2
Estimate of the standard deviation of x, ~
4, i> +t
in-n 4
oe ON yg
Confidence interval for 2, — jy using the ¢ distribution:
(H — %2) Ets,
‘Test statistic using the 7 distribution:
7%) — (Hr = #2)
RT
+ For two independent samples selected from (wo populations
with unequal and unknown standard deviations:
eV Ty
Confidence interval for 4, — M2 using the ¢ distribution:
Ga 7 m2) + ts
‘Test statistic using the r distribution:
=) ~ = Ha)
Say
+ For two paired or matched samples:
Sample mean for paired differences: d = Zd/n
Sample standard deviation for paired differences:
zd}?
[ae SF
n
Na
Mean and standard deviation of the sampling distribution
ofd:
Ha = He and 33 = 5,/Vn
Confidence interval for yw, using the # distribution:
d © ty where 39 = ,/Va
Test statistic for a test of hypothesis about 414 using the t
distribution:
= Me
Sa
+ For two large and independent samples, confidence interval
for py — py:
t
(Br — Ba) * zsp.—p, where 55g, =
+ For two large and independent samples, for a test of
hypothesis about p, — p, with Hy: p, ~ p, = 0:
Pooled sample proportion:
=_utn mp, + mpr
Be
my + ny my + ny
Estimate of the standard deviation of 6, ~ 2:
aT
(Lh, +)
ny
Test statistic:
Chapter 11 - Chi-Square Tests
+ Expected frequency for a category for a gondness-of-fit
test:
E=np
+ Degrees of freedom for a goodness-of-fit test:
df=k-1
+ Expected frequency for a cell for an independence or ho-
mogencily Lest:
where & is the number vf calegories
(Row total)(Column total)
Sample size
+ Degrees of freedom for a test of independence or
homogeneity:
df= R-WC-1)
where & and C are the total number of rows and columns,
respectively, in the contingency table i
i
