Confidence level C
The success rate of the method that produces the confidence interval. In C% of all possible
samples, the method would yield an interval that captures the true parameter value.
Confidence interval
An interval calculated from sample data, which has the general form estimate � margin of error or, alternatively, statistic � (critical value)(standard deviation of statistic).
The critical value depends on both the confidence level C and the sampling dis
Margin of error
Tells how close the estimate tends to be to the unknown parameter in repeated random sampling.
One-sample t interval for a population mean
Choose an SRS of size n from a population having unknown
mean � is (mean x) � (t)(Sx/sqrt(n))
where t* is the critical value for the t distribution with df = n - 1. Use this interval only when: (1) the population
distribution is Normal or the sample size
One-sample z interval for a population mean
Draw an SRS of size n from a population having unknown
mean ? and known standard deviation ?. As long as the Normal and Independent conditions are met, a level C confidence interval for ? is
(mean x) � (z*)(st. dev./sqrt(n))
The critical value z* is found
Point estimate
The specific value of a point estimator.
Point estimator
A statistic that provides an estimate of a population parameter.
Robust procedures
An inference procedure is called robust if the probability calculations involved in that procedure remain fairly accurate when a condition for using the procedure is violated.
Standard error
When the standard deviation of a statistic is estimated from data, the result is the standard error of the statistic.
Standard error of the sample proportion p^
([p^](1-p^)/n). It describes how far p^ will be from p, on average, in repeated SRSs of size n.
Standard error of the sample mean x
(Sx)(sqrt(n)) where Sx is the sample standard deviation. It describes how far mean x will be from � , on average, in repeated SRSs of size n.
The t distributions; degrees of freedom
Draw an SRS of size n from a large population that has a Normal distribution with mean ? and standard deviation ?. The statistic
t=(mean x-�)/(Sx/sqrt(n)) has the t distribution with degrees of freedom df = n - 1. This statistic will have approximately a
Degrees of freedom
The number of values that can vary in a stats calculation