Question

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.

Answer 1

The conditions for inference are met, and the school board can proceed with constructing a confidence interval.

Step-by-step explanation:

To determine if the conditions for inference are met, we need to check if the random sample condition, the 10% condition, and the large counts condition are satisfied.

The random sample condition is met because the sample households were selected randomly.

The 10% condition is met because the sample size of 100 households is less than 10% of the total households in the district.

The large counts condition is met because both the number of households that support starting the school year a week earlier (43) and the number of households that do not support it are greater than 10.

Therefore, the conditions for inference are met and the school board can proceed with constructing a 95% confidence interval for the proportion of households that would support starting the school year a week earlier.