Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
-Refer to Exhibit 12-6. The calculated value for the test statistic equals
A)300
B)4
C)0

Question

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.  
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
-Refer to Exhibit 12-6. The calculated value for the test statistic equals
A)300 
B)4 
C)0

Quizplus · Accepted Answer

To test for uniform distribution, we can use the chi-squared goodness-of-fit test. The formula for the test statistic is

X^2 = sum[(O-E)^2/E]

where O is the observed frequency and E is the expected frequency. In this case, we would expect each group to have 100 individuals if the opinions are uniformly distributed.

The expected frequency for each group is 100, and the observed frequencies are 90, 110, and 100.

Using the formula, we get:

X^2 = [(90-100)^2/100] + [(110-100)^2/100] + [(100-100)^2/100] 
     = 20/10 + 10/10 + 0/10 
     = 3

Using a chi-squared distribution table with two degrees of freedom (since we have three groups and one parameter was estimated from the data), we find that the critical value for a 0.05 level of significance is 5.99.

Since our calculated value (3) is less than the critical value (5.99), we fail to reject the null hypothesis that the opinions are uniformly distributed. Therefore, D is the correct answer.

Exhibit 12-6 The Following Shows the Number of Individuals in a Sample