## 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 ...