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 determine if it is equally likely that the Dow Jones Industrial Average will go up each day of the week, we need to perform a chi-square goodness-of-fit test.

The null hypothesis is that the Dow Jones Industrial Average is equally likely to go up on each day of the week, and the alternative hypothesis is that it is not equally likely.

We use the formula for chi-square goodness-of-fit test:

χ2 = Σ (Observed frequency - Expected frequency)2 / Expected frequency

where Σ denotes the sum of the values.

To calculate the expected frequency for each day of the week, we find the total number of days that the Dow Jones Industrial Average went up and divide by 5 (since there are 5 weekdays). So, the expected frequency for Monday is (49/5)=9.8, Tuesday is (39/5)=7.8, Wednesday is (46/5)=9.2, Thursday is (47/5)=9.4, and Friday is (40/5)=8.

Using the given data and expected frequencies, we get:

χ2 = [(12-9.8)2/9.8] + [(9-7.8)2/7.8] + [(13-9.2)2/9.2] + [(8-9.4)2/9.4] + [(8-8)2/8]

χ2 = 0.605

Looking at the chi-square distribution table with 4 degrees of freedom (since we have 5 categories and one parameter was estimated), the critical value at the 0.05 significance level is 9.488.

Since our calculated chi-square value (0.605) is less than the critical value (9.488), we fail to reject the null hypothesis that the Dow Jones Industrial Average is equally likely to go up on each day of the week.

Therefore, the answer is D) 2.57.

A Fund Manager Wants to Know If It Is Equally