1

Problem

The results of two random samples of votes for a proposition are shown above. The samples were selected from the same population, and the margins of error were calculated using the same method. Which of the following is the most appropriate reason that the margin of error for sample A is greater than the margin of error for sample B?

2

Step

Sample Size:

→ Generally, larger sample sizes result in smaller margins of error because larger samples provide more precise estimates of the population parameter.

3

Step

Variability in Responses:

→ Higher variability in responses within a sample can lead to larger margins of error because it indicates less consistency in the population’s opinions or behaviors.

4

Step

Given that the samples were selected from the same population and the margins of error were calculated using the same method, we can focus on the differences between the two samples.

5

Step

Here’s how we can approach the solution:
Analyze Sample A and Sample B:

→ Examine the sample sizes of both samples.
→ Consider any differences in the variability of responses between the two samples.

6

Step

Identify the Reason for the Difference in Margin of Error:

→ Select the option that aligns with the identified reason for the difference in margin of error.

7

Step

Let’s say:

→ Sample A has a smaller sample size compared to Sample B.
→ Both samples exhibit similar variability in responses.

8

Step

In this case, the most appropriate reason for the margin of error for sample A being greater than the margin of error for sample B would be the difference in sample sizes.

9

Solution

Therefore, the solution is "Sample A had a smaller sample size.

10

Sumup

Please summarize steps

Choices

11

Choice-A

The margin of error is primarily affected by sample size, not by unrecorded votes

Wrong Sample A had a smaller number of votes that could not be recorded

12

Choice-B

The percentage of favorable responses does not directly impact the margin of error. The sample size is the key factor

Wrong Sample A had a higher percentage of favorable responses

13

Choice-C

A larger sample size reduces the margin of error, so this option contradicts the question’s premise

Wrong Sample A had a larger sample size

14

Choice-D

Smaller sample sizes lead to larger margins of error because there is more variability in estimates when fewer data points are collected

Correct Sample A had a smaller sample size

15

Answer

Option

D

16

Sumup

Please summarize choices