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?

Question

GPT-4o mini · Answer

To calculate the number of failures in this scenario, we first need to identify the number of successes and total sample size.

In the given scenario:

Total sample size (n) = 225
Proportion of individuals in favor (p) = 28% = 0.28

The number of successes (individuals in favor) can be calculated as: \[ \text{Number of successes} = n \times p = 225 \times 0.28 = 63 \]

Now, to find the number of failures, we subtract the number of successes from the total sample size: \[ \text{Number of failures} = n - \text{Number of successes} = 225 - 63 = 162 \]

Therefore, the number of failures in this scenario is 162.