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Conventional home smoke alarms have too often failed to awaken sleeping children--they are remarkably resistant to being awakened by sound, even in the daytime! Researchers are studying the possibility that a personalized "voice" smoke alarm would be more effective than mere sound. The idea is that a recording of the mother's voice calling the child's name may be an improvement over existing systems.
a)The researchers would like to estimate p to within 0.05 with 95% confidence. Past experience has shown that conventional alarms are effective about 0.58 of the time. If this is accepted as a reasonable initial estimate of p, what sample size should they use for their study?
b)Suppose the researchers felt that the original study, done with children of parents working in a single hospital, was different enough so that their results (p = 0.58) should not be relied upon. In a few sentences, explain how your procedure for choosing a samples size would differ from your solution in part (a). (Do NOT recalculate a new estimate of the necessary sample size!)
Income Level
The amount of monetary or material wealth that an individual, family, or group receives, usually quantified on an annual basis.
Chocolate-Covered Peanuts
Peanuts that have been coated in a layer of chocolate, serving as a sweet and crunchy snack.
Preference
An individual's choice or inclination towards a specific option among a set of alternatives based on tastes, utility, or desirability.
Coconuts
Tropical fruit known for its water and flesh, often used as food and in various products, representing a good in economics.
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