A specific numerical value estimate of a parameter. The best point estimate of the population mean μ is the sample mean x̄.
An interval or a range of values used to estimate the parameter.
A range of values constructed from sample data so that parameter occurs within that range at a specified probability. The specified probability is called the level of confidence.
The maximum likely difference between the point estimate of a parameter and the actual value of the parameter.
Minimum sample size needed for an interval estimate of the population mean, when n ≥ 30.
|
Situation |
n ≥ 30 | n < 30 σ known |
n < 30 σ unknown |
|
Test |
Z |
Z |
t |
| CI |
 |
 |
|
When testing for = or ≠, α need to be divided by 2.
Thus, Zα/2 are used. Otherwise, use Zα.
If σ is unknown, replace by s.
Testing Hypothesis is a statistical hypothesis, in which states if there are differences between a parameter and a specific value, or between two parameters.
Null hypothesis, H0 states that there are no differences in between.
Alternative hypothesis, H1 states that there are differences in between.
A statistical test uses the data obtained from a sample to make the decision about the null hypothesis that should be rejected or not. The numerical value obtained from a statistical test is called the test value.
| Accept H0 | Reject H0 | |
| H0 is true | Correct | Type I Error |
| H0 is false | Type II Error | Correct |
The probability of type I error is denoted by α.
The probability of type II error is denoted by β.
The maximum probability of committing a type I error, thus α is the rejection region.
An interval or a range of values used to estimate the parameter.