Question

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The calculated value for the test statistic equals a. 20. b. 4. c. 2. d. -2.

Answer 1

Answer:

$\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The expected values for all the categories is :

$E_i =\frac{150}{3}=50$

And then the statistic would be given by:

$\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4$

And the best option would be:

b. 4

Step-by-step explanation:

For this problem we have the following observed values:

Yes 40 No 60 No Opinion 50

And we want to test the following hypothesis:

Null hypothesis: All the opinions are uniformly distributed

Alternative hypothesis: Not All the opinions are uniformly distributed

And for this case the statistic would be given by:

$\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The expected values for all the categories is :

$E_i =\frac{150}{3}=50$

And then the statistic would be given by:

$\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4$

And the best option would be:

b. 4