INFERENTIAL STATISTICS
Recall that descriptive statistics is the branch of statistics in charge of collecting, organizing,
analyzing, interpreting, presenting data in a manner that is easy to understand by any audience,
even by those with little or no sta
Critcal Values of t
The table entries represent the critical values of t
for the specified value of the shaded area () in the
right tail of the Student's t Distribution.
0
0.025
0.020
0.010
0.005
0.0025
0.001
t
DF
0.250
0.200
0.150
0.100
0.050
0.0005
0.00
Critcal Values of 2
(Continued)
The table entries represent the critical values of 2
for the specified value of the shaded area () in the
right tail of the Chi Square Distribution.
2
0
0.9500
0.9000 0.8750 0.8500
0.8000 0.7500
0.7000
0.6000
0.003932
0.015
5] TESTS OF HYPOTHESIS
TESTING HYPOTHESES (ABOUT THE POPULATION MEAN )
4.1] LARGE SAMPLES (n 30), ANY POPULATION (Normally Distributed or Not)
Left-Tailed Test
Right-Tailed Test
Two-Tailed Test
Null Hypothesis:
Alternative:
Ho: = o
Ha: < o
Ho: = o
Ha: > o
4] THE SAMPLING DISTRIBUTION OF
( x 1 x 2)
1) Two random samples of size 25 each are obtained from two different populations. Population 1 has mean
86 and standard deviation 12. Population 2 has mean 94 and standard deviation 17. Let x 1 represent the
mea
[6] TWO-PARAMETER TESTS OF HYPOTHESES
[6.1] LARGE SAMPLES OR NORMALLY DISTRIBUTED POPULATIONS
TEST STATISTICS:
z=
( x1 x 2 ) ( 1 2 )
12
n1
+
2
2
or
n2
( x1 x 2 ) ( 1 2 )
2
s12 s2
+
n1 n2
ASSUMPTIONS: Samples are independent simple random samples. If the
Areas of a Standard Normal Distribution
The table entries represent the area under the
standard normal curve from 0 to the specified
value of z
0
z
z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3