MATH 1040 Exam 4

Probability Value (p-value)

Assuming the null hypothesis is true, probability of obtaining a sample statistic with a value as extreme or more extreme Than one determined from the sample data.

Null Hypothesis Ho

A statement if no change

An alternate hypothesis Ha

Is a statement of change or difference

Type 1 error

Occurs when we reject the null and accept the alternative when the null is true. (Action)

Type 2 error

Occurs when we fail to reject the null when the null is true (inaction)

Level of significance

Maximum allowable probability of making a type I error. Denoted by a, alpha.

Test statistic

Is compared to the parameter in the null hypothesis

Standardized test statistic

Is a converted test statistic when assuming the null hypothesis is true

If p < σ,

Reject Ho

If p > σ,

Fail to reject Ho

Left-tailed test

Is one of three types of test. The Ha contains a < and the p value is left of the test statistic.

Right-tailed

Is one of three types of test. The Ha contains a > and the p value is right of the test statistic.

Two tailed test

Is one of three types of test. The Ha contains a ≠ and half the p value is left of the test statistic and half is to the right of the test statistic.

Rejection region (aka the critical region)

Is a range of values for which the null hypothesis is not probable. The critical value divides the rejection region from the non-rejection region

Left tailed alt hypothesis:

<

Right Tailed alt Hypothesis:

>

Two tailed alt hypothesis

≠

Z test for mean μ

Is a statistical hypothesis test for a population mean where the decision is based on data.

Ζ calc =

x̄ - μο / σ / √n

T-calc=

x̄ - μο / s / √n

p̂ =

x / n

z-calc =

p̂ - po / √po•qo /n

X²-calc =

(n-1) • s² / o²

Independent Sampling

The sample selected from one population is not related to a sample selected from a second population

Dependent Sampling

Are two paired or matched samples that correspond

μ(x̄1-x̄2) =

μ1-μ2

Ζcalc =

(x̄1-x̄2) / √ σ²(1) / n - σ²(2) / n