General

Point Estimate

A specific numerical value estimate of a parameter. The best point estimate of the population mean μ is the sample mean x̄.

 

Interval Estimate

An interval or a range of values used to estimate the parameter.

 

Confidence Interval (CI)

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.

 

Maximum error of estimate

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.

 

Level of Significance

The maximum probability of committing a type I error, thus α is the rejection region.

 

Critical Value (CV)

The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected.

 

Compare CV with the test statistics:

 

P-value

The probability value is the actual area under the standard distribution curve, representing the probability of a particular sample statistic, or if the statistic occurring if the null hypothesis is true.

 

If p < α, reject the null hypothesis.

 

Procedure

State the hypotheses and identify the claim.

Set H0 and H1.

 

Check assumptions and conditions.

Independence and normality.

 

Find the critical values and rejection region.

One-sided or two-sided rejection region

 

Compute the test value.

Z test or t test

 

Decide whether the null hypothesis is rejected or not and draw the conclusion.

H0 is rejected or not.

There is (in)sufficient evidence that ...