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Table 6.1 Results of mutual fund sample
Fund types frequency
Investor risk
preference
Bond
Income
Income/Growth
Growth
Totals
Risk-taker
30
9
45
66
150
Conservative
270
51
75
54
450
Totals
300
60
120
120
600
two categorical ( nominal ) variables. Ultimately, we would like to know if the result
can be extended to the entire population, or is due simply to chance. For exam-
ple, consider the relationship between two variables: (1) an investor’s self-perceived
behavior toward investing, and 2) the selection of mutual funds made by the investor.
This test is known as the Chi-square , or Chi-squared, test of independence .Asthe
name implies, the test addresses the question of whether or not the two categorical
variables are independent (not related).
Now let us consider a specific example. A mutual fund investment company sam-
ples a total of 600 potential investors who have indicated their intention to invest
in mutual funds. The investors have been asked to classify themselves as either
risk-taking or conservative investors. Then, they are asked to identify a single type
of fund they would like to purchase. Four fund types are specified for possible
purchase and only one can be selected— bond , income , growth , and income and
growth . The results of the sample are shown in Table 6.1. This table structure is
known as a contingency table and this particular contingency table happens to have
2 rows and 4 columns—a 2 by 4 contingency table. Contingency tables show the
frequency of occurrence of the row and column categories. For example, 30 (first
row /first column) of the 150 ( Totals row for risk-takers) investors in the sample that
identified themselves as risk-takers said they would invest in a bond fund, and 51
(second row/second column) investors considering themselves to be conservative
said they would invest in an income fund. These values are counts or the frequency
of observations associated with a particular cell.
6.3.1 Tests of Hypothesis—Null and Alternative
The mutual fund investment company is interested in determining if there is a rela-
tionship in an investor’s perception of his own risk and the selection of a fund that the
investor actually makes. This information could be very useful for marketing funds
to clients and also for counseling clients on risk tailored investments. To make this
determination, we perform an analysis of the data contained in the sample. The anal-
ysis is structured as a test of the null hypothesis . There is also an alternative to the
null hypothesis called, quite appropriately, the alternative hypothesis . As the name
implies, a test of hypothesis, either null or alternative, requires that a hypothesis is
 
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