A local school board wants to determine if the proportion of households in the district that would support starting the school year a week earlier has changed from the previous year. Last year, the school board determined that 65 percent of households supported starting school earlier. They ask a random sample of 100 households this year, and 70 percent state they would support starting the school year earlier. The cap p -value for the test of the hypotheses, ratio of cap h sub 0 to p is equal to 0 point 6 5 and ratio of cap h sub A to p is not equal to 0 point 6 5 , is 0 point 2 9 What is the correct interpretation of this value?
Answer
A
Assuming 65 percent of households would support starting school earlier, there is a 0 point 2 9 probability of getting a sample proportion of 0 point 7 0 or more different from 0 point 6 5 .
B
Assuming this sample was collected correctly, the probability of getting 70 households out of 100 that would support starting school earlier is 0 point 2 9 if 65 percent of households truly support starting school earlier.
C
Only 29 percent of households in this sample approve of starting school earlier.
D
Assuming 65 percent or more households would support starting school earlier, there is a 0 point 2 9 probability of getting a sample proportion of 0 point 7 0 or more different from 0 point 6 5 .
Explanation
A p-value is calculated assuming the null hypothesis is true: here, that 65% of households support starting school earlier. Because the alternative is two-sided, the p-value is the probability of getting a sample proportion at least as far from 0.65 as the observed 0.70, in either direction. That probability is 0.29, so choice A is correct. Choice B describes getting exactly 70 supporters, rather than a result at least as extreme as the observed one.
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