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Week Five Lecture Part II – A Summary
Here is a summary of the statistical applications and their characteristics we have
learned and used in RES/342.
z Test Statistic
The z test statistic is applied when we are testing the hypothesis of the difference
between two population means, and the standard deviation is known. The z test statistic
is based on a z score (measures the number of standard deviations that a data value is
from the mean). The z test statistic assumes a normal distribution, thus measures of
central tendency apply. In using the z test statistic we need a minimum of 30
observations from which the sample is selected. We refer this then to a large sample.
Any number of observations less than 30 is referred to as a small sample. Finally, we
apply the test statistic value to determine if our sample value is “statistically significant.”
We must decide how statistically significant we want any sample to be. If we are ok with
accepting that the sample is in 95% of the observations, then we would chose a 0.05
level of significance, which means, we accept the willingness to be wrong in the long
run 5 % of the time. The level of significance then determines the rejection region where
the null hypothesis is not supported. We use the standard normal table to determine
those boundaries. At a level of significance of 0.05, that means the rejection region is +
or – 1.96. Our decision to accept our null hypothesis is based on whether or not the test
statistic value (of our sample) is inside the + and 1.96.
Tailed tests are involved with this test statistic. Here is a summary of the three
possibilities:
Twotailed tests.
Used when the test statistic could be a negative value or a
positive value. The scenario situation is worded so that we are interested in only
determining if one population is
different
than another. The word
different
means that
the value of one could be higher or lower than the other. The hypothesis set up,
therefore is:
H
O
:
μ
1
=
2
H
A
:
1
≠
2
Lowertail test
. Used when the test statistic is testing the mean of one population
sample to determine if it is
less than
the other parameter. The hypothesis set up,
therefore is:
H
O
:
1
≥
2
H
A
:
1
<
2
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View Full Document Uppertail test
. Used when the test statistic is testing the mean of one population
sample to determine if it is
greater than
the other parameter. The hypothesis set up,
therefore is:
H
O
:
μ
1
≤
2
H
A
:
1
>
2
Although we are attempting to prove support for the null hypothesis, we can see
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This note was uploaded on 10/10/2010 for the course STATS Stats301 taught by Professor Regis during the Spring '10 term at DeVry Irvine.
 Spring '10
 Regis
 Statistics

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