Chapter 9 : Significance Tests about Hypotheses
Significance tests
or
Tests of Hypotheses
is another important method of statistical inference
alongside point and interval estimation.
A
Hypothesis
is a statement about one or more population parameters .
Eg
: A statement
about the population mean μ may be denoted by H: u=7
(On an average, UF students studies 7 hours during the week)
A
Significance test
is a method by which it is decided whether the above statement about
the parameter is supported by the data observed from a random sample.
Any significance test has five distinct steps viz
•
Making Assumptions
: The most important assumption is that the data result from a
randomized experiment
or a random sample. Other assumptions relate to
sample size
and
shape
of the population distribution.
•
Constructing Hypothesis
: Each significance test is composed of
2
hypothesis :
H
0
(
Null
Hypothesis)
: It is a statement that specifies a particular value
of the parameter determined from
experience
or
prior belief
.
Ha (
Alternate
Hypothesis)
: It states that the population parameter
falls in some alternative range of values. So, it is a statement of change. It may be
one
or
two
sided.
Ex 1:
Visitor records show that, during 2008, on an average, about 25 visitors visited
Kanapaha Botanical gardens
per day. Since then some beautification has been done and
the park management suspects that the number of visitors may have increased. Thus,
our null hypothesis will be
Ho: u=25
and the alternative hypothesis will be
Ha: u>25
Here,
μ
denotes the population mean number of
visitors to the park per day in 2008. Here the
alternative hypothesis is
one sided
.
Eg
2
: Historically in Canada, the proportion of adults who favour legalized gambling has
been 0.50. The government wants to know whether the mindset of
adults has changed
(for better or for worse) during recent times. So, our null hypothesis will be
Ho: p=.50
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View Full Documentand the alternative hypothesis will be
Ha: p not equal to .50
Here p is the
population proportion of adults who favor legalized gambling at present.
Here Ha is a
two sided
hypothesis.
•
Determining the Test statistic
: A test statistic measures how
close
the
point
estimate
of the parameter is to the
null hypothesis
value(of the parameter). This “closeness” is measured in terms of the
standard error
of the estimate. Thus, it is given by
( Parameter estimate null hypothesis)/ standard error
•
Calculating the pvalues :
This is the probability of getting a test statistic value more
extreme than what we have actually got given that the null hypothesis
is true.
A small pvalue would indicate that our test statistic takes a value which is very
unlikely under the
null hypothesis. So, maybe the null hypothesis itself is
(o.w our test statistic would not have been what it is).
Thus, smaller
p values represent
stronger
evidence against H
0
.
•
Drawing conclusion
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 Spring '08
 TA
 Statistics, Normal Distribution, Null hypothesis, Statistical hypothesis testing, Kanapaha Botanical

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