Chi Square Test Example Problems With Answers Pdf
When it comes to statistical analysis, the chi-square test is a widely used tool. It is a non-parametric statistical test that is used to determine the degree of association between two categorical variables. In this article, we will go over some chi square test example problems with answers pdf so you can understand how the test works and how to apply it in practice.
What is the Chi Square Test?
The chi-square test is a statistical test used to determine the association between two categorical variables. It is a non-parametric test, which means that it does not rely on any assumptions about the distribution of the data. Instead, it is based on the observed frequencies of the data.
The test compares the observed frequency distribution of a categorical variable with the expected frequency distribution. The expected frequency distribution is calculated based on the null hypothesis that there is no association between the two variables.
There are two types of chi-square tests: the chi-square goodness-of-fit test and the chi-square test for independence. The chi-square goodness-of-fit test is used to test whether a sample of categorical data follows a population distribution. The chi-square test for independence is used to test whether two categorical variables are independent.
Chi Square Goodness of Fit Test Example
The chi-square goodness-of-fit test is used to test whether a sample of categorical data follows a population distribution. Let’s say we want to test whether a six-sided die is fair, meaning that each side has an equal chance of being rolled. We roll the die 60 times and record the following results:
| Side | Frequency | Expected Frequency | (F - E)² / E |
|---|---|---|---|
| 1 | 13 | 10 | 0.9 |
| 2 | 10 | 10 | 0 |
| 3 | 11 | 10 | 0.1 |
| 4 | 8 | 10 | 0.4 |
| 5 | 6 | 10 | 1.6 |
| 6 | 12 | 10 | 0.4 |
To calculate the expected frequency, we divide the total number of rolls (60) by the number of sides on the die (6), which gives us 10. We then calculate the chi-square statistic by summing up the values in the fourth column. The chi-square statistic in this case is 3.4.
To determine whether the die is fair or not, we compare the chi-square statistic to the critical value of the chi-square distribution with 5 degrees of freedom and a significance level of 0.05. The critical value in this case is 11.07. Since the chi-square statistic is less than the critical value, we fail to reject the null hypothesis that the die is fair.
Chi Square Test for Independence Example
The chi-square test for independence is used to test whether two categorical variables are independent. Let’s say we want to test whether there is a relationship between gender and smoking status. We survey 200 people and record the following results:
| Gender | Smoker | Non-Smoker |
|---|---|---|
| Male | 40 | 60 |
| Female | 30 | 70 |
To perform the chi-square test for independence, we first calculate the expected frequency for each cell in the contingency table. We do this by multiplying the row total by the column total and dividing by the grand total. For example, the expected frequency for male smokers is (40+60) x (40+30) / 200 = 40. We then calculate the chi-square statistic by summing up the values in the fourth column. The chi-square statistic in this case is 1.26.
To determine whether there is a relationship between gender and smoking status, we compare the chi-square statistic to the critical value of the chi-square distribution with 1 degree of freedom and a significance level of 0.05. The critical value in this case is 3.84. Since the chi-square statistic is less than the critical value, we fail to reject the null hypothesis that gender and smoking status are independent.
Conclusion
The chi-square test is a powerful statistical tool that can be used to determine the degree of association between two categorical variables. In this article, we have gone over some chi square test example problems with answers pdf so you can see how the test works in practice. Remember to use caution when interpreting the results of the chi-square test and to always consider the context in which the test was performed.
