Anita Gill 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, the appropriate decision is ___.
A)reject the null hypothesis and conclude the two variables are not independent
B)reject the null hypothesis and conclude the two variables are independent
C)do not reject the null hypothesis and conclude the two variables are not independent
D)do not reject the null hypothesis and conclude the two variables are independent
E)do nothing

Question

Anita Gill 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, the appropriate decision is ___.
A)reject the null hypothesis and conclude the two variables are not independent 
B)reject the null hypothesis and conclude the two variables are independent 
C)do not reject the null hypothesis and conclude the two variables are not independent 
D)do not reject the null hypothesis and conclude the two variables are independent 
E)do nothing

Quizplus · Accepted Answer

We can use a chi-square test for independence to determine whether there is a relationship between industry sector and investment objective. With a significance level of 0.01 and the given contingency table, we obtain a chi-square test statistic of 22.95. Comparing this to a chi-square distribution table with degrees of freedom equal to (3-1)(2-1)=2, we find that the critical value is 9.21. Since our test statistic is greater than the critical value, we reject the null hypothesis and conclude that the two variables are not independent, meaning that industry sector does influence investment objective.

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

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