A local school board wants to determine the proportion of households in the district that would support starting the school year a week earlier. They ask a random sample of 100 households whether they would support starting the school year a week earlier, and 43 households responded that they would. The school board plans to construct a 95% confidence interval for the true proportion of households that would support starting the school year a week earlier.

Are the conditions for inference met?

A) Yes, the conditions for inference are met.
B) No, the 10% condition is not met.
C) No, the randomness condition is not met.
D) No, the Large Counts Condition is not met.

The conditions for constructing a 95% confidence interval are met because the sample is random, represents less than 10% of the population, and both np and n(1-p) are at least 10. Correct option is a).

To determine whether the conditions for inference are met for constructing a 95% confidence interval for the true proportion of households that would support starting the school year a week earlier, we have to check several conditions:

The sampling method must be random. It is assumed the question refers to a random sample, hence the randomness condition is met.
The 10% condition requires that the sample be less than 10% of the population. Unless the total number of households in the district is less than 1,000, this condition is met as well.
The Large Counts Condition requires that both np and n(1-p) be at least 10, where n is the sample size and p is the sample proportion. In this case, n = 100 and p = 0.43, so np = 43 and n(1-p) = 57, which are both greater than 10.

Since all these conditions are satisfied, the answer is:

A)Yes, the conditions for inference are met.