Exam 8: Interval Estimates for Proportions, Mean Differences and Proportion Differences

In a matched sample design, one uses the average for each pair of data values when building a confidence interval.

In a 95% confidence interval estimate of the difference between two population means, the standard error of the proportion will be 1.96 times the margin of error.

For large enough sample sizes, 95% of the possible sample mean differences will be within 1.96 standard errors of the population mean difference.

When calculating the sample size to use in estimating a population proportion, using a proportion equal to 0.25 will provide the maximum sample size.

When each data value in one sample is paired with a corresponding data value in another sample, the samples are said to be independent.

For the sampling distribution of the sample proportion, the distribution is approximately normal as long as n < 30.

One of the properties of the sampling distribution of the sample proportion is that the expected value of the sample proportion will be exactly equal to 0.5.

In the absence of any other information, determining the largest sample size that might be necessary to build a 95% confidence interval estimate of a population proportion requires us to assume that the population proportion $\pi$ is .50.

A 95% confidence interval estimate of the difference between two population proportions will contain 95% of the possible sample proportion differences.

In a 95% confidence interval estimate of a population proportion, the margin of error will be 2.33 times the standard error of the proportion.

As the sample size increases, the margin of error in an interval estimate of a population proportion decreases.

In any confidence interval estimate of a population proportion difference, the margin of error will be less than the standard error of the sampling distribution.

A matched sample design can lead to a smaller sampling error than the independent sample design because some or all of the variation between sampled items is eliminated as a source of sampling error.

An interval estimate of a population proportion is a range of values used to estimate the population parameter $\pi$ .

As the confidence requirement increases, the standard error term in an interval estimate of the difference between two population proportions decreases.

The value of $\pi$ that maximizes the product $\pi$ (1 - $\pi$ ) is .05.

The sampling distribution of the sample proportion is the probability distribution of all possible values of the sample proportion when a sample of size n is taken from a particular population.

The sampling distribution of the sample mean difference is the probability distribution of all possible values of the sample mean difference when a sample of size n₁ is taken from one population and a sample of size n₂ is taken from another.

In determining a confidence interval for the difference between two population proportions, the point estimate of the difference is ( - ).