Exam 9: Estimation Using a Single Sample

A newspaper recently conducted a survey of a random sample of 120 registeredvoters in order to predict the winner of a local election. The Republican candidatewas preferred by 62 of the respondents.Assuming that it is reasonable to regard the 120 voters in the sample as representativeof the population of voters, construct and interpret a 90% confidence interval for theproportion of registered voters who prefer the Republican candidate.

The margin of error of a statistic defines the minimum likely estimationerror.

One difficulty in measuring the nesting success of birds is that the researchers mustcount the number of eggs in the nest, which is disturbing to the parents. Even thoughthe researcher does not harm the birds, the flight of the bird might alert predators tothe presence of a nest. To see if researcher activity might degrade nesting success,the nest survival of 102 nests that had their eggs counted, was recorded. Sixty-four ofthese nests failed (meaning the parent abandoned the nest.) Assuming that it is reasonable to regard the 102 nests in the sample as representativeof the population of nests for which the eggs have been counted, construct andinterpret a 95% confidence interval for the proportion of nests that have eggs countedthat are then abandoned.

In a couple sentences, define a "biased statistic" and "unbiased statistic." What is thedifference between the two?

Under what conditions is it reasonable to use the z confidence interval to estimate apopulation proportion?

What is the standard error of a statistic, and what information does it provide?

In a few sentences, identify the two desirable characteristics of a good estimator, andexplain what makes them desirable characteristics.

An understanding of choices of habitat is an important element in understanding thebiology and ecology of birds. One aspect of habitat choice is the pattern of preferredvertical height when feeding in forests. In a study of small birds in an old-growthforest in the Pacific Northwest, researchers, suspended from a giant crane, observedthe landings of Golden-crowned kinglets (Regulus strapa). They found that 78 of the163 landings were in the "mid" height region of trees, 21-40 meters above ground. a) Compute an estimate of the population proportion of all landings of these kingletsthat are in the 21 - 40 meter height range. b) Based on the data above, what is the margin of error of ˆp ?

The large sample confidence interval formula for estimating p can safelybe used whenever n ? 30.