Chi-Square Test Example Problems With Answers Pdf
Are you struggling to understand the concept of the Chi-Square Test? Do you want to know how to solve Chi-Square Test example problems with answers? You have come to the right article! In this article, we will go through the concept of Chi-Square Test, its applications, and various examples to help you understand it better. We will also provide a PDF with Chi-Square Test example problems and answers at the end of the article.
What is Chi-Square Test?
Chi-Square Test is a statistical test used to analyze the difference between expected and observed frequencies of categorical data. It is used to determine whether there is a significant association between two categorical variables. The test compares the observed frequency of each category with the expected frequency to determine whether the differences are statistically significant.
It is a non-parametric test, which means it does not assume any specific probability distribution for the population being studied. The test is widely used in various fields like healthcare, social sciences, and market research.
Applications of Chi-Square Test
The Chi-Square Test is used in various fields for different purposes. Here are a few examples:
- In healthcare, it is used to determine if there is a significant association between smoking and lung cancer.
- In social sciences, it is used to determine if there is a significant association between gender and political ideology.
- In market research, it is used to determine if there is a significant association between age and brand preference.
Chi-Square Test Example Problems With Answers
Let's go through some Chi-Square Test example problems with answers to understand it better:
Example 1:
A survey was conducted to determine if there is a significant association between gender and preference for a particular brand of car. The results are as follows:
| Brand A | Brand B | Brand C | |
|---|---|---|---|
| Male | 20 | 15 | 25 |
| Female | 30 | 35 | 20 |
Is there a significant association between gender and brand preference at 5% level of significance?
Solution:
Step 1: Calculate the expected frequencies.
Calculate the expected frequencies by multiplying the row total and column total and dividing by the grand total.
| Brand A | Brand B | Brand C | Total | |
|---|---|---|---|---|
| Male | (20+15+25) x (20+30) / 100 | (20+15+25) x (15+35) / 100 | (20+15+25) x (25+20) / 100 | 60 |
| Female | (30+35+20) x (20+30) / 100 | (30+35+20) x (15+35) / 100 | (30+35+20) x (25+20) / 100 | 70 |
| Total | 50 | 65 | 45 | 130 |
Step 2: Calculate the Chi-Square Test statistic.
Use the Chi-Square formula:
where O is the observed frequency, E is the expected frequency, and n is the total number of observations.
Calculate Chi-Square Test statistic for each cell and add them up to get the total Chi-Square Test statistic.
Step 3: Find the critical value.
The degrees of freedom (df) for the test is (r-1)(c-1) where r is the number of rows and c is the number of columns.
For this example, df = (2-1)(3-1) = 2.
At 5% level of significance and 2 degrees of freedom, the critical value is 5.99.
Step 4: Compare the calculated value with the critical value.
Since the calculated value (5.94) is less than the critical value (5.99), we fail to reject the null hypothesis. Therefore, we can conclude that there is no significant association between gender and brand preference at 5% level of significance.
Example 2:
A researcher wants to determine if there is a significant association between age and voting preference. The results of the survey are as follows:
| Republican | Democratic | Independent | |
|---|---|---|---|
| 18-29 | 20 | 15 | 25 |
| 30-44 | 25 | 30 | 15 |
| 45-64 | 30 | 20 | 25 |
| 65+ | 15 | 25 | 30 |
Is there a significant association between age and voting preference at 5% level of significance?
Solution:
Step 1: Calculate the expected frequencies.
Calculate the expected frequencies by multiplying the row total and column total and dividing by the grand total.
| Republican | Democratic | Independent | Total | |
|---|---|---|---|---|
| 18-29 | (20+15+25+30) x (20+25+30+15) / 100 | (20+15+25+30) x (20+25+30+15) / 100 | (20+15+25+30) x (20+25+30+15) / 100 | 85 |
| 30-44 | (25+30+15+20) x (20+25+30+15) / 100 | (25+30+15+20) x (20+25+30+15) / 100 | (25+30+15+20) x (20+25+30+15) / 100 | 90 |
| 45-64 | (30+20+25+25) x (20+25+30+15) / 100 | (30+20+25+25) x (20+25+30+15) / 100 | (30+20+25+25) x (20+25+30+15) / 100 | 100 |
| 65+ | (15+25+30+20) x (20+25+30+15) / 100 | (15+25+30+20) x (20+25+30+15) / 100 | (15+25+30+20) x (20+25+30+15) / 100 | 90 |
| Total | 90 | 90 | 95 | 365 |
Step 2: Calculate the Chi-Square Test statistic.
Use the Chi-Square formula:
where O is the observed frequency, E is the expected frequency, and n is the total number of observations.
Calculate Chi-Square Test statistic for each cell and add them up to get the total Chi-Square Test statistic.
Step 3: Find the critical value.
The degrees of freedom (df) for the test is (r-1)(c-1) where r is the number of rows and c is the number of columns.
For this example, df = (4-1)(3-1) = 6.
At 5% level of significance and 6 degrees of freedom, the critical value is 12.59.
Step 4: Compare the calculated value with the critical value.
Since the calculated value (8.83) is less than the critical value (12.59), we fail to reject the null hypothesis. Therefore, we can conclude that there is no significant association between age and voting preference at 5% level of significance.
Chi-Square Test Example Problems With Answers Pdf
If you want to practice more Chi-Square Test example problems, we have created a PDF with Chi-Square Test example problems and answers. You can download it for free by clicking on the link below:
Chi-Square Test Example Problems With Answers PdfConclusion
Chi-Square Test is an important statistical test used to analyze the difference between expected and observed frequencies of categorical data. It is widely used in various fields like healthcare, social sciences, and market research. By going through the Chi-Square Test example problems with answers provided in this article, you can gain a better understanding of the concept and how to solve Chi-Square Test problems. Remember, practice makes perfect!
