Download Chapter 8 Confidence interval for p The confidence interval for p is

Chapter 8
Confidence interval for p
The confidence interval for p is the probability that p lies in the interval between p hat minus the
margin of error and p hat plus the margin of error.
(For more information, review Section 8.3)
Confidence interval for the population mean
A c confidence interval for the population mean is an interval computed from sample data in such
a way that c is the probability of generating an interval containing the actual value of the
population mean.
(For more information, review Section 8.1)
Confidence level c
The reliability of an estimate is measured by the confidence level. Suppose we want a confidence
level of c. Theoretically, you can choose c to be any value between 0 and 1, but usually c is
equal to a number such as 0.90, 0.95, or 0.99.
(For more information, review Section 8.1)
Critical value zc
For a confidence level c, the critical value zc is the number such that the area under the standard
normal curve between -zc and zc equals c.
(For more information, review Section 8.1)
Degrees of freedom
Values of the variable t corresponding to what we call the number of degrees of freedom,
abbreviated d.f. For the methods used in this section, the number of degrees of freedom is given
by the formula d.f. = n - 1 where d.f. stands for the degrees of freedom and n is the sample
size. Each choice for d.f. gives a different t distribution.
(For more information, review Section 8.2)
Margin of error
The margin of error is the magnitude (i.e. the absolute value) of the difference between the
sample point estimate and the true population parameter value.
(For more information, review Section 8.1)
Maximal margin of error
The margin of error is the magnitude of the difference between the sample mean and the
population mean. In most practical problems, the population mean is unknown, so the margin of
error is also unknown. However, we can compute an error tolerance E that serves as a bound on
the margin of error. Using a c% level of confidence, we can say that the point estimate differs
from the population mean by a maximal margin of error. The maximal margin of error is zc
multiplied by the population standard deviation and divided by the square root of the sample
size.
(For more information, review Section 8.3)
Point estimate
A point estimate of a population parameter is an estimate of the parameter using a single
number. A sample mean is a point estimate of the population mean.
(For more information, review Section 8.1)
Point estimate for p, p hat
For a binomial distribution, p hat is the number of successes divided by the number of trials. This
can be used as a point estimate for p, the population proportion of successes.
(For more information, review Section 8.3)
The Student's t variable
The Student's t variable is calculated by starting with the sample standard deviation divided by
the square root of the sample size. Then subtract the population mean from the sample mean,
and divide the result by the previously calculated value.
(For more information, review Section 8.2)