Is there any relationship between the age of an investor and the rate of return

Question

Is there any relationship between the age of an investor and the rate of return that the investor expects from an investment? A random sample of 972 common stock investors was selected, and each investor was placed in one of four age categories and in one of four categories according to rate believed attainable ("Patterns of Investment Strategy and Behavior Among Individual Investors, " Journal of Business [1977]: 296-333). The resulting data are given in the following table: Does there appear to be an association between age and rate of return believed attainable? Test the appropriate hypotheses using a.01 significance level.

Explanation / Answer

applying chi square goodness of fit on above:

for abvoe X2 stat =103.870

for 0.01 level and (4-1)*(4-1)=9 degree of freedom ; critical value =21.67

as test stat is higher then critical value ; we reject null hypothesis that there is not association b/w age and return

And Conclude that there is strong evidence of association b/w age and return

Observed O 0-5% 6-10% 11-15% >15% Total <45 15 51 51 29 146 45-54 31 133 70 48 282 55-64 59 139 35 20 253 65> 84 157 32 18 291 Total 189 480 188 115 972 Expected E=rowtotal*column total/grand total 0-5% 6-10% 11-15% >15% Total <45 28.389 72.099 28.239 17.274 146 45-54 54.833 139.259 54.543 33.364 282 55-64 49.194 124.938 48.934 29.933 253 65> 56.583 143.704 56.284 34.429 291 Total 189 480 188 115 972 chi square =(O-E)^2/E 0-5% 6-10% 11-15% >15% Total <45 6.315 6.174 18.346 7.960 38.796 45-54 10.359 0.281 4.380 6.420 21.441 55-64 1.954 1.583 3.968 3.296 10.801 65> 13.284 1.230 10.477 7.840 32.832 Total 31.913 9.269 37.172 25.517 103.870

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