In a small town of 5,832 people, the mayor wants to determine the proportion of voters who would support an increase to the food tax. An assistant to the mayor decides to survey 1,000 randomly chosen people to construct a 90% confidence interval for the true proportion of people who would support the increase in food tax. Of the sample, 363 people say they would support the increase. Are the conditions for inference met?

The sample was randomly chosen, so the randomness condition is met. The Large Counts Condition is also met: 363 people support the increase and 1,000 − 363 = 637 do not, and both counts are at least 10. However, the 10% condition requires the sample size to be no more than 10% of the population: 0.10 × 5,832 = 583.2. Since 1,000 exceeds 583.2, the 10% condition is not met, so the correct choice is “No, the 10% condition is not met.”

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