A group of participants was surveyed and the information collected shown in the partially completed contingency table below regarding gender and attitudes on abortion. Firstly, calculate the missing values.  

 
Support

Oppose

Undecided

Total

Female

314

242

68

U

Male

V

W

102

936

Total

785

X

Y

Z

Now, using the completed contingency table, select the statements from the following list that are **true**.   Note: a statement is true only if the value you calculated from the completed contingency table, when rounded to the same number of decimal places as in the statement, is the same as the value in the statement. 

To solve this problem, we need to complete the contingency table by calculating the missing values first. Once the table is completed, we can verify the truthfulness of any statements regarding the data. Here's the plan:

### Step 1: Set Up the Known Values

The contingency table is partially filled as follows:

|              | Support | Oppose | Undecided | Total |
|--------------|---------|--------|-----------|-------|
| **Female**   | 314     | 242    | 68        | U     |
| **Male**     | V       | W      | 102       | 936   |
| **Total**    | 785     | X      | Y         | Z     |

### Step 2: Calculate the Missing Values

1. **Calculate \( U \)**: The total number of females is the sum of the Support, Oppose, and Undecided categories for females:
   \[
   U = 314 + 242 + 68 = 624
   \]

2. **Calculate \( V \)**: The number of males who support is calculated by subtracting the number of females who support from the total number of people who support:
   \[
   V = 785 - 314 = 471
   \]

3. **Calculate \( Z \)**: The total number of participants is given as the total number of males plus the total number of females:
   \[
   Z = 936 + 624 = 1560
   \]

4. **Calculate \( X \)**: The number of participants who oppose is calculated by subtracting the number of females who oppose from the total number of people who oppose:
   \[
   X = 1560 - 785 - Y
   \]
   Since \( Y \) is not yet known, we need to calculate \( Y \) first.

5. **Calculate \( Y \)**: The number of undecided participants is the sum of undecided males and females:
   \[
   Y = 102 + 68 = 170
   \]

6. **Now Calculate \( X \)**: Given that \( Y = 170 \), we can calculate \( X \):
   \[
   X = 1560 - 785 - 170 = 605
   \]

7. **Calculate \( W \)**: The number of males who oppose is calculated by subtracting the number of females who oppose from the total number of people who oppose:
   \[
   W = X - 242 = 605 - 242 = 363
   \]

### Step 3: Complete the Contingency Table

Now the completed table is:

|              | Support | Oppose | Undecided | Total |
|--------------|---------|--------|-----------|-------|
| **Female**   | 314     | 242    | 68        | 624   |
| **Male**     | 471     | 363    | 102       | 936   |
| **Total**    | 785     | 605    | 170       | 1560  |

### Step 4: Verify Statements

Based on the calculations, you can now verify any given statements regarding the data. To proceed further, you would need the list of statements to compare against these calculated values.

Would you like me to verify specific statements based on this completed table or provide further analysis? Here are some related questions:

1. How can we calculate the proportion of females who support abortion?
2. What is the percentage of males who are undecided?
3. How can we use the chi-square test to assess the independence between gender and attitudes on abortion?
4. What is the marginal distribution of the "Oppose" category?
5. How does the overall support rate compare to the rate among females?

**Tip:** When analyzing contingency tables, always ensure that the row and column totals match their corresponding sums from the data provided.

Learn how to solve a contingency table problem involving gender and attitudes on abortion. This detailed solution covers calculating missing values, completing the table, and verifying statements based on the data. Suitable for undergraduate level statistics.

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