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 find the chi-square value, we need to first calculate the expected values for each cell using the formula:
expected value = (row total x column total) / grand total

The expected values for each cell are:

- Technology & Electronics: (83 x 71) / 200 = 29.495
- Healthcare: (41 x 71) / 200 = 14.495
- Finance & Insurance: (48 x 71) / 200 = 17.04
- Retail: (28 x 71) / 200 = 9.94

The total expected value is 71.97.

The chi-square test statistic is calculated by summing the squared difference between the observed and expected values for each cell, divided by the expected value, for all four cells. This gives:

((54-29.495)^2 / 29.495) + ((33-14.495)^2 / 14.495) + ((41-17.04)^2 / 17.04) + ((72-9.94)^2 / 9.94) = 32.885

Using a significance level of 0.01 with 3 degrees of freedom (4 - 1 - 1 = 2), we look up the critical value in the chi-square distribution table to be 9.210. Since our observed chi-square value (32.885) is greater than the critical value (9.210), we reject the null hypothesis and conclude that there is a significant association between industry sector and investment objective.
 
Therefore, the best choice is C.

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

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