I need help with the critical value. Should I reject the null hypothesis or fail

Question

I need help with the critical value. Should I reject the null hypothesis or fail to reject? A survey was taken on how a lump-sum pension would be invested by 45-year-olds and 65-year-olds. The are shown here. At alpha a o os, is there a relationship between the age of the investor and the way the money would be invested? data Round Predicted values to the nearest integer. Also, show all s steps of a hypothesis test Large Small Inter. CDs or company company national money stock stock stock market funds funds funds funds Bonds s s s Age 45 20 15 45 Age 65 42 6 24 as o H.: here no 5.84. 21.17

Explanation / Answer

Given table data is as below

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calculation formula for E table matrix

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expected frequecies calculated by applying E - table matrix formulae

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

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set up null vs alternative as
null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =9.4877
since our test is right tailed,reject Ho when ^2 o > 9.4877
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 27.9973
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 5 - 1 ) = 1 * 4 = 4 is 9.4877
we got | ^2| =27.9973 & | ^2 | =9.4877
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0
ANSWERS
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null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w age of the investor and the way money would be invested
test statistic: 27.9973
critical value: 9.4877
p-value:0
decision: reject Ho      
we have evidence to support,exists a relation b/w age of the investor and the way money would be invested                  

col1 col2 col3 col4 col5 row 1 20 10 10 15 45 100 row 2 42 24 24 6 24 120 TOTALS 62 34 34 21 69 N = 220

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