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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 [tex] p_s [/tex] be the true proportion of households with school-aged children that would support starting the school year a week early and [tex] p_w [/tex] be 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?

A. The random condition is not met.
B. The 10% condition is not met.
C. The Large Counts Condition is not met.
D. All conditions for inference are met.

Answer :

Answer: I believe the correct answer is "The Large Counts Condition is not met."

Step-by-step explanation: To check that it's not being met you use the condition [tex]n(1-p) \geq 10[/tex]. where n is sample size and p is the expected probability of success. The fails for their survey of parents with school aged children. Using n = 40 and p = [tex]\frac{38}{40}[/tex], this condition is not met. [tex]40(1-\frac{38}{40}) = 2[/tex].

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