• Point Estimate and Interval Estimate
An interval estimate is an interval of numbers within which
the parameter value is believed to fall.
A point estimate is a single number that is our “best guess”
for the parameter.
• Confidence Interval
A confidence interval is an interval containing the most
believable values for a parameter. The probability that this
method produces an interval that contains the parameter is
called the confidence level. This is a number chosen to be
close to 1, most commonly 0.95
• Margin of Error
The margin of error measures how accurate the point
estimate is likely to be in estimating a parameter. It is a
multiple of the standard error of the sampling distribution of
the estimate, such as 1.96×(standard error) when the
sampling distribution is a normal distribution.
A 95% confidence interval for a population proportion p is
p
p̂ ± 1.96(se), with se = p̂(1 − p̂)/n
where p̂ denotes the sample proportion based on n observations.
z-Scores for the Most Common Confidence Levels
Confidence Level
0.90
0.95
0.99
Error Probability
0.10
0.05
0.01
z-Score
1.645
1.96
2.58
Confidence Interval
p̂ ± 1.645(se)
p̂ ± 1.96(se)
p̂ ± 2.58(se)
Effects of Confidence Level and Sample Size on Margin of Error
The margin of error for a confidence interval:
• Increases as the confidence level increases
• Decreases as the sample size increases.
A 95% confidence interval for the population mean µ is
√
x̄ ± t.025,df (se), with se = s/ n
where t.025,df denotes the t-score of the t-distribution and
df = n − 1 denotes the degrees of freedom of the corresponding
t-distribution.