Question

# You want to know whether people in different regions of the country are equally likely to vote Sarah Duterte, Peter Cayetano, Mar Roxas, or any candid

Chi-square tests
You want to know whether people in different regions of the country are equally likely to vote Sarah Duterte, Peter Cayetano, Mar Roxas, or any candidate other than the three in the next election. You would use
A. chi-square test of independence.
B. either chi-square test (goodness-of-fit or test of independence), depending on how you set up the problem.
C. chi-square goodness-of-fit test.
D. both chi-square tests, in order to check the results of one with the other.

2020-12-10
Step 1
The Chi-Square Test of Independence determines whether there is an association between categorical variables (i.e., whether the variables are independent or related). It is a nonparametric test.
This test is also known as:
-Chi-Square Test of Association.
This test utilizes a contingency table to analyze the data. A contingency table (also known as a cross-tabulation, crosstab, or two-way table) is an arrangement in which data is classified according to two categorical variables.
The categories for one variable appear in the rows, and the categories for the other variable appear in columns. Each variable must have two or more categories. Each cell reflects the total count of cases for a specific pair of categories.
Chi-Square goodness of fit test is a non-parametric test that is used to find out how the observed value of a given phenomena is significantly different from the expected value. In Chi-Square goodness of fit test, the term goodness of fit is used to compare the observed sample distribution with the expected probability distribution. Chi-Square goodness of fit test determines how well theoretical distribution (such as normal, binomial, or Poisson) fits the empirical distribution. In Chi-Square goodness of fit test, sample data is divided into intervals. Then the numbers of points that fall into the interval are compared, with the expected numbers of points in each interval.
Step 2
Since, we are to test whether people in different regions of the country are equally likely to vote Sarah Duterte, Peter Cayetano, Mar Roxas, or any candidate other than the three in the next election we will use Chi-Square goodness of fit test.
A Chi-Square for goodness of fit test is a test used to assess whether the observed data can be claimed to reasonably fit the expected data. Sometimes, a Chi-Square test for goodness of fit is referred as a test for multinomial experiments, because there is a fixed number of N categories, and each of the outcomes of the experiment falls in exactly one of those categories. Then, based on sample information, the test uses a Chi-Square statistic to assess if the expected proportions for all categories reasonably fit the sample data. The main properties of a one sample Chi-Square test for goodness of fit are:
- The distribution of the test statistic is the Chi-Square distribution, with n-1 degrees of freedom, where n is the number of categories
- The Chi-Square distribution is one of the most important distributions in statistics, together with the normal distribution and the F-distribution
The formula for a Chi-Square statistic is
$$\displaystyle{x}^{{2}}={\sum_{{{i}={1}}}^{{n}}}\frac{{{\left({O}_{{i}}-{E}_{{i}}\right)}^{{2}}}}{{E}_{{i}}}$$
One of the most common uses for this test is to assess whether a sample come from a population with a specific population(this is, for example, using this test we can assess if a sample comes from a normally distributed popelation or not).