(b) Provide A Table With The Expected Counts For Each Of The Four Categories. Round Your Answers To Two Decimal Places.$[ \begin{tabular}{|c|cc|} \hline & \multicolumn{1}{|c}{Metal} & Electronic \ \hline Survived & 44.20 & 50.80 \ Died &
In this section, we will provide a table with the expected counts for each of the four categories: Metal, Electronic, Survived, and Died. We will round our answers to two decimal places.
Understanding the Problem
The problem requires us to provide a table with expected counts for each of the four categories. This means we need to calculate the expected frequencies for each category based on the given data.
Calculating Expected Counts
To calculate the expected counts, we need to use the concept of expected frequencies. The expected frequency for each category is calculated by multiplying the row total by the column total and dividing by the grand total.
Let's assume we have the following data:
| Metal | Electronic | Total | |
|---|---|---|---|
| Survived | 44.20 | 50.80 | 95.00 |
| Died | 55.80 | 64.20 | 120.00 |
| Total | 100.00 | 115.00 | 215.00 |
Expected Counts Table
| Metal | Electronic | Total | |
|---|---|---|---|
| Survived | 44.20 | 50.80 | 95.00 |
| Died | 55.80 | 64.20 | 120.00 |
| Total | 100.00 | 115.00 | 215.00 |
Calculating Expected Counts for Each Category
To calculate the expected counts for each category, we will use the following formula:
Expected Count = (Row Total x Column Total) / Grand Total
Let's calculate the expected counts for each category:
Metal Category
- Expected Count for Survived: (95.00 x 100.00) / 215.00 = 44.19
- Expected Count for Died: (120.00 x 100.00) / 215.00 = 55.81
Electronic Category
- Expected Count for Survived: (95.00 x 115.00) / 215.00 = 50.79
- Expected Count for Died: (120.00 x 115.00) / 215.00 = 64.21
Survived Category
- Expected Count for Metal: (95.00 x 100.00) / 215.00 = 44.19
- Expected Count for Electronic: (95.00 x 115.00) / 215.00 = 50.79
Died Category
- Expected Count for Metal: (120.00 x 100.00) / 215.00 = 55.81
- Expected Count for Electronic: (120.00 x 115.00) / 215.00 = 64.21
Expected Counts Table with Calculations
| Metal | Electronic | Total | |
|---|---|---|---|
| Survived | 44.19 | 50.79 | 95.00 |
| Died | 55.81 | 64.21 | 120.00 |
| Total | 100.00 | 115.00 | 215.00 |
Conclusion
In this section, we will provide a Q&A article to help clarify any doubts or questions you may have about the expected counts for each category.
Q: What are expected counts?
A: Expected counts are the calculated frequencies for each category based on the given data. They are used to determine how likely it is for a particular category to occur.
Q: How are expected counts calculated?
A: Expected counts are calculated by multiplying the row total by the column total and dividing by the grand total.
Q: What is the formula for calculating expected counts?
A: The formula for calculating expected counts is:
Expected Count = (Row Total x Column Total) / Grand Total
Q: Why are expected counts important?
A: Expected counts are important because they help us understand how likely it is for a particular category to occur. They can also be used to identify any patterns or trends in the data.
Q: Can you provide an example of how to calculate expected counts?
A: Let's say we have the following data:
| Metal | Electronic | Total | |
|---|---|---|---|
| Survived | 44.20 | 50.80 | 95.00 |
| Died | 55.80 | 64.20 | 120.00 |
| Total | 100.00 | 115.00 | 215.00 |
To calculate the expected counts for each category, we would use the following formula:
Expected Count = (Row Total x Column Total) / Grand Total
For example, to calculate the expected count for the Metal category and the Survived category, we would use the following formula:
Expected Count = (95.00 x 100.00) / 215.00 = 44.19
Q: How do I interpret the expected counts table?
A: The expected counts table shows the calculated frequencies for each category. The table is divided into four sections: Metal, Electronic, Survived, and Died. Each section shows the expected count for each category.
Q: Can I use the expected counts table to make predictions?
A: Yes, the expected counts table can be used to make predictions. By analyzing the expected counts, you can identify any patterns or trends in the data and make predictions about future events.
Q: Are there any limitations to using expected counts?
A: Yes, there are several limitations to using expected counts. Expected counts are based on the assumption that the data is normally distributed, which may not always be the case. Additionally, expected counts may not take into account any underlying relationships between the variables.
Q: Can I use expected counts in conjunction with other statistical methods?
A: Yes, expected counts can be used in conjunction with other statistical methods, such as regression analysis or hypothesis testing. By combining expected counts with other statistical methods, you can gain a more comprehensive understanding of the data.
Conclusion
In this Q&A article, we have provided answers to some of the most frequently asked questions about expected counts. We have also provided examples and explanations to help clarify any doubts or questions you may have. understanding expected counts, you can gain a deeper understanding of the data and make more informed decisions.