Point estimate

A single number that is used to estimate the value of an unknown parameter

Margin of error

Describes how close it is likely to be to the population mean
Multiply critical value by standard error

Critical value

Positive Z-score that corresponds to confidence interval
1 - ? is the confidence level expressed as a decimal, then the
critical value is Z?/2 because the area under the normal curve between
-Z?/2 and Z?/2 is 1 - ?

Confidence interval

An interval that is used to estimate the value of a parameter
We must have a simple random sample with a large (n>30) sample
size or population is approximately normal

Confidence level

A percentage between 0% and 100% that measures the success rate of
the method used to construct the confidence interval

Procedure for constructing a confidence interval for ? when ? is knkown

Find the value of the point estimate if it isn't given
Find the critical value corresponding to the desired confidence
level from the last row of A.3 from table A.2
Find the standard error ?/?n multiply it by the critical value to
obtain the margin of error Z?/2 (?/?n)
Use the point estimate and the margin of error to construct the
confidence interval

Sample size needed

n= ((Z?/2*?)/m)^2
Round up to the nearest whole number

Student's t Distribution

number of degrees of freedom = n-1
Critical value is t?/2 and can be found in table A.3
We have a simple random sample with a large sample size (n>30) or
population is approximately normal

Assumptions for constructing a confidence interval for P

We have a simple random sample
The population is at least 20 times as large as the sample
The items in the population are divided into two categories
The sample must contain at least 10 individuals in each category

Procedure for constructing a confidence interval for P

Compute the value of the point estimate p?
Find the critical value Z?/2 corresponding to the desired confidence
level, either from the last line of table A.3 or from table A.2
Compute the standard error ?(p?(1-p))/n and multiply it by critical
value Z?/2 to obtain margin of error
Use point estimate and margin of error to construct the confidence interval

Sample size needed for p?

n=p?(1-p?)(Z?/2/m)^2
Round up to nearest whole number.

Confidence intervals with small samples

p?=(x+2)/(n+4)

Determining which method to use