Question

A small town with a population of 1,200 residents held elections for the position of mayor. Four candidates had announced their candidature for the election. On the day of the election, a local newspaper conducted an exit poll near two polling booths with two groups of 100 residents each. The results are given in the table shown below.

Name Group A Group B
Chris Jones 51 29
Patrick Smith 6 4
Michael Small 30 54
Susan Davis 13 13


Which of the following statements about the data above is true?
A.
The estimated number of residents who would have voted for Michael Small is higher for Group B than Group A.
B.
The estimated number of residents who would have voted for Susan Davis is higher for Group A than Group B.
C.
The estimates for both groups show an equal number of residents would have voted for Michael Small.
D.
The estimated number of residents who would have voted for Michael Small is higher for Group A than Group B.

Answer 1

To evaluate the statements about the data from the exit poll, we first need to calculate the estimated number of voters for each candidate based on the responses from Group A and Group B. Since each group has 100 residents, we can directly interpret the numbers as the percentage of votes in that group.

**Calculations:**

1. **Chris Jones:**
- Group A: 51 votes
- Group B: 29 votes

2. **Patrick Smith:**
- Group A: 6 votes
- Group B: 4 votes

3. **Michael Small:**
- Group A: 30 votes
- Group B: 54 votes

4. **Susan Davis:**
- Group A: 13 votes
- Group B: 13 votes

Now we analyze each candidate:

- For **Michael Small**:
- Group A: 30 votes (30% of 100)
- Group B: 54 votes (54% of 100)
- Conclusion: 30 < 54, so **Group B has a higher estimated number of residents** who would have voted for Michael Small than Group A.

- For **Susan Davis**:
- Group A: 13 votes (13% of 100)
- Group B: 13 votes (13% of 100)
- Conclusion: Susan Davis has an **equal number of estimated votes** in both groups.

Now let's evaluate each statement:

A. The estimated number of residents who would have voted for Michael Small is higher for Group B than Group A.
**True** - (30 < 54)

B. The estimated number of residents who would have voted for Susan Davis is higher for Group A than Group B.
**False** - (13 = 13)

C. The estimates for both groups show an equal number of residents would have voted for Michael Small.
**False** - (30 ≠ 54)

D. The estimated number of residents who would have voted for Michael Small is higher for Group A than Group B.
**False** - (30 < 54)

The correct answer is **A: The estimated number of residents who would have voted for Michael Small is higher for Group B than Group A.**