A local school board believes there is a difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 38 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 35 respond yes. Let ps= the true proportion of households with school-aged children that would support starting the school year a week early and pw= the true proportion of households without school-aged children that would support starting the school year a week earlier. Which of the following is a correct statement about the conditions for this test?
The random condition is not met.
The 10% condition is not met.
The Large Counts Condition is not met.
All conditions for inference are met.
The random condition is met since the samples were chosen randomly from the population.
The 10% condition is met since the sample sizes are both less than 10% of their respective populations.
The Large Counts Condition is also met since np > 10 and n(1-p) > 10 for both samples.
Therefore, all conditions for inference are met.