Chapter 6

c-Confidence Interval for a Population Proportion p

A c-confidence interval for a population proportion p is ___ where ___. The probability that the confidence interval contains p is c, assuming that the estimation process is repeated a large number of times.

Point Estimate

A point estimate is a single value estimate for a population parameter. The most unbiased point estimate of the population mean u is the sample mean x.

C-Confidence Interval for a Population Mean U

A c-confidence interval for a population mean u is ___. The probability that the confidence interval contains u is c, assuming that the estimation process is repeated a large number of times.

Interval Estimate

An interval estimate is an interval, or range of values, used to estimate a population parameter.

Margin of Error E

Given a level of confidence c, the margin of error E (sometimes also called the maximum error of estimate or error tolerance) is the greatest possible distance between the point estimate and the value of the parameter it is following. All of these conditions have to be met: 1. The sample is random. 2. At least one of the following is true: the population is normally distributed or n is greater than or equal to 30.

t-Distribution

If the distribution of a random variable x is approximately normal, then ___ follows a t-distribution. Critical values of t are denoted by tc. Here are several properties of the t-distribution: 1. The mean, median, and mode of the t-distribution are equal to 0. 2. The t-distribution is bell-shaped and symmetric about the mean. 3. The total area under the t-distribution curve is equal to 1. 4. The tails in the t-distribution are "thicker" than those in the standard normal distribution. 5. The standard deviation of the t-distribution varies with the sample size, but it is greater than 1. 6. The t-distribution is a family of curves, each determined by a parameter called the degrees of freedom. The degrees of freedom (sometimes abbreviated as d.f.) are the number of free choices left after a sample statistic such as x is calculated. When you use a t-distribution to estimate a population mean, the degrees of freedom are equal to one less than the sample size. 7. As the degrees of freedom increase, the t-distribution approaches the standard normal distribution, as shown in the figure. For 30 or more degrees of freedom, the t-distribution is close to the standard normal distribution.

Level of Confidence C

The level of confidence c is the probability that the interval estimate contains the population parameter, assuming that the estimation process is repeated a large number of times.

Point Estimate for p

The point estimate for p, the population proportion of successes, is given by the proportion of successes in a sample and is denoted by ___ where x is the number of successes in the sample and n is the sample size. The point estimate for the population proportion of failures is q = 1 - p. The symbols p and q are read as "p hat" and "q hat."