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Hypothesis Testing
HypothesisTesting Null Hypothesis Test statistic
Testing hypothesis about
population means Ho: μ = or > or < specified value
i. s is known & population is normal Normal: z
ii. s is known & sample size is 30 Normal: z
Ho: μ = or > or < specified value
population is normal but s is not known t statistic: t
Testing hypothesis about
population proportions Ho: p= or > or < specified valuei. If binomial probabilities can be calculated
i.e. n, the no. of trials & p probability of
success should be given; sample size should
be ≤ 500 binomial
ii. If n > 500, then normal approximation is
used Normal: z
Testing hypothesis about
population variance Ho: s2= or > or < specified value Chi square: c2
Testing hypothesis with
respect to comaprison of
paired observations Ho: μ1 - μ2 <, = or > 0 Paired t
Testing hypothesis for
differences between
population means Ho: μ1 - μ2 <, = or > a particular value
i. when sample sizes n1 & n2 are both
atleast 30 & population std. deviations s1 &
s2 are known ii.
Both populations are normally distributed &
the population std. deviations s1 & s2 are
known Normal: z
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iii. Both populations are normally
distributed, population std. deviations are
unknown but both sample standard
deviations are known t statistic
Testing hypothesis for
differences between two
population proportions for
large samples
Ho: p1ᶺ - p2ᶺ <, = or > zero or a particular
value Normal: z
Testing hypothesis for
equality of two population
variances Ho: s12
= s22
F distribution
ANOVA Ho: μ1 = μ2 = μ3
Note: Pls refer Complete Business Statistics by Amir Aczel & J. Sounderpandian pg - 295- 352
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Formula
(x bar - m)/ sn
(x bar - m)/ sn
(x bar - m)/ sn
P (X = x) =ncx .p
x.q
n-x
pᶺ -p0/p0 (1-p0)/n}
(n-1)S2/s0
2
t = {(x1 bar - x2 bar) - (μ1 - μ2)o}/sp(1/n1+1/n2)
where sp is the combined standard deviation of the two samples given
as sp = [(n1-1) s12
- (n2-1)s22/(n1-1)+(n2-1)]
z = {(x1 bar - x2 bar) - (m1 m2)(s12n1) + (s22n2)
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t = {(x1 bar - x2 bar) - (m1 m2)sp2(1n1 + 1n2)
z = {(p1ᶺ - p2ᶺ) - (p1 - p2)o}/pᶺ(1-pᶺ)(1/n1+1/n2)} where pᶺ =(x1 + x2)/(n1 + n2)
F = (c12/k1
)/(c22/k2
) where c1
2is a chi-square random variable with k1 df
& c22
is another independent chi-square variable with k2 df
for further reference
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Non - parametric test: these are used mainly
when population distributrions are not
normal
Sign test
Mann Whitney U test
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Kruskal-Wallis
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