Exam 9: Estimation Using a Single Sample

The size of the population does need to be considered if sampling is without replacement and the sample size is more than 10% of the population size. In this case, a finite population correction factor is used to adjust the margin of error (the given margin is multiplied by the correction factor). Since this correction factor is always less than 1, the adjusted margin of error is smaller.

When choosing a statistic for computing an estimate, what factors should be considered?

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 π 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 π, 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!)

A random sample of 150 employees was selected. There are 60 employees older than 30 in the sample. Estimate the proportion of all employees of the company who are older than 30 with a 50% confidence. ​

Under what conditions is it reasonable to use the t confidence interval to estimate a population mean?

All else being equal, the higher the confidence level, the wider the confidence interval.