Question

A researcher wants to create a confidence interval for the proportion of residents in a city who support roadwork being conducted only at night. She selects a random sample of 225 residents and asks whether they are in favor of roadwork being conducted only at night. The proportion of individuals in favor of roadwork being conducted at night is 28 percent. What is the number of failures in this scenario?(1 point)

Answer 1

To determine the number of failures in this scenario, we need to first identify what a "failure" indicates in the context of the research.

In this case, a "failure" is considered to be an individual who does not support roadwork being conducted only at night.

Given:

• Sample size (n) = 225 residents
• Proportion in favor (p) = 28% = 0.28

To find the number of successes (those in favor), we can calculate: \[ \text{Number of successes} = p \times n = 0.28 \times 225 = 63.0 \]

Thus, the number of individuals in favor of the roadwork at night is approximately 63.

Now, to find the number of failures: \[ \text{Number of failures} = n - \text{Number of successes} = 225 - 63 = 162 \]

Therefore, the number of failures is 162.