Conventional Home Smoke Alarms Have Too Often Failed to Awaken

question 8

Essay

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!)

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Definitions:

Portfolio Weight

The percentage composition of a particular holding or investment relative to the total value of the portfolio.

Expected Return

The forecasted amount of profit or loss an investment is projected to generate, expressed as a percentage of the total invested capital.

Portfolio Weight

The percentage composition of a particular holding in relation to the total value of the portfolio, used to assess diversification and risk.

Security Market Line

A graphical representation in financial market theory that depicts the relationship between risk (measured as beta) and expected return for the entire market.