A fund manager wants to know if it is equally likely that the Dow Jones Industrial Average will go up each day of the week. For each day of the week, the fund manager observes the following number of days when the Dow Jones Industrial Average goes up. Which of the following is the value of goodness-of-fit chi-square test statistic?
A) 0.605
B) 0.632
C) 1.62
D) 2.57

Question

A fund manager wants to know if it is equally likely that the Dow Jones Industrial Average will go up each day of the week. For each day of the week, the fund manager observes the following number of days when the Dow Jones Industrial Average goes up.  Which of the following is the value of goodness-of-fit chi-square test statistic?
A) 0.605 
B) 0.632 
C) 1.62 
D) 2.57

Quizplus · Accepted Answer

To test if it is equally likely that the Dow Jones Industrial Average will go up each day of the week, we need to use a goodness-of-fit chi-square test. 
The expected frequency for each day of the week is 35/5 = 7, since there are 35 total observations and 5 days in a week.
Now we can calculate the chi-square test statistic:
$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$
where $O_i$ is the observed frequency and $E_i$ is the expected frequency.
The calculations are as follows:
$\chi^2 = \frac{(12-7)^2}{7} + \frac{(5-7)^2}{7}+ \frac{(6-7)^2}{7}+ \frac{(5-7)^2}{7}+ \frac{(7-7)^2}{7}= 2.57$
Using a chi-square distribution table with 4 degrees of freedom (5 - 1), we find that the critical value at a 5% significance level is 9.49. Since the calculated chi-square statistic is less than the critical value, we fail to reject the null hypothesis that the Dow Jones Industrial Average is equally likely to go up each day of the week.

A Fund Manager Wants to Know If It Is Equally