Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective.Her staff prepared the following contingency table from a random sample of 200 common stocks.
Using $\alpha$ = .01,observed chi-square value is ______________.
A) 24.93
B) 8.17
C) 32.89
D) 6.59
E) 4.89

Question

Anita Cruz recently assumed responsibility for a large investment portfolio. She wonders whether industry sector influences investment objective.Her staff prepared the following contingency table from a random sample of 200 common stocks.  
Using $\alpha$ = .01,observed chi-square value is ______________.
A) 24.93 
B) 8.17 
C) 32.89 
D) 6.59 
E) 4.89

Quizplus · Accepted Answer

To calculate the chi-square value, we need to first find the expected frequency for each cell. This can be done by multiplying the row total and column total and then dividing by the grand total. For example, the expected frequency for the first cell is (51*74)/200 = 18.87. 
Once we have the expected frequency for each cell, we can calculate the chi-square value using the formula: 
(∑(O-E)^2/E) 
where O is the observed frequency and E is the expected frequency. 
After performing the calculations, we get an observed chi-square value of 32.89, which exceeds the critical value of 6.635 (lookup in chi-square table with 11 degrees of freedom and alpha level of 0.01). Therefore, we reject the null hypothesis and conclude that there is a significant relationship between industry sector and investment objective.

Anita Cruz Recently Assumed Responsibility for a Large Investment Portfolio α\alphaα

Anita Cruz Recently Assumed Responsibility for a Large Investment Portfolio $\alpha$