Exam 9: Estimation Using a Single Sample

One difficulty in measuring the nesting success of birds is that the researchers must count the number of eggs in the nest, which is disturbing to the parents. Even though the researcher does not harm the birds, the flight of the bird might alert predators to the 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 of these nests failed (meaning the parent abandoned the nest.) Assuming that it is reasonable to regard the 102 nests in the sample as representative of the population of nests for which the eggs have been counted, construct and interpret a 95% confidence interval for the proportion of nests that have eggs counted that are then abandoned.

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

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

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

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

The width of the confidence interval for p decreases as the sample size increases.

A z of 1.96 is used when calculating 95% large-sample confidence intervals for p.

The standard error of $\hat { p } \text { is } \sqrt { n p ( 1 - p ) }$

In a very large school district, student records have been kept in three distinct data bases, one each for elementary, middle, and high school. The district now has a new data base and wishes to correct any original data entry errors. To allocate enough secretarial time to this task, an estimate of the proportion of records that contain errors must be made. Initial estimates are that there are fixable errors in about 15% of the records. A) Using 15% as an initial estimate of the percentage of records with errors, compute the sample size required to estimate the true proportion of records with errors within .025 with 95% confidence. B) Suppose the school district did not have an initial estimate of p . 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!)