8.1: Hypothesis testing basics

Question 1

null hupothesis H0

Answer 1

The hypothesis that the researcher wants to reject (always includes the equal to condition

Question 2

Alternative hypothesis Ha

Answer 2

What is concluded if there is sufficient evidence to reject the null hypothesis and is usually what you are really trying to assess. Why? You can never really prove anything with statistics—when the null hypothesis is discredited, the implication is that the alternative hypothesis is valid.

Question 3

The decision rule

Answer 3

(rejection rule) for a two-tailed z-test at α = 0.05 can be stated as follows:

Reject H0 if test statistic < –1.96 or test statistic > 1.96

Two-Tailed Hypothesis Test Using the Standard Normal (z) Distribution shows the standard normal distribution for a two-tailed hypothesis test using the z-distribution.

Question 4

test statistic

Answer 4

difference between the sample statistic and the hypothesized value, scaled by the standard error of the sample statistic:

Question 5

Hypothesis testing involves two statistics:

Answer 5

the** test statistic** calculated from the sample data and (2) the critical value of the test statistic. The value of the computed test statistic relative to the critical value is a key step in assessing the validity of a hypothesis.

Question 6

significance level

Answer 6

probability of making a Type I error (rejecting the null when it is true) and is designated by the Greek letter alpha (α).

Significance level of 5% (α = 0.05) means there is a 5% chance of rejecting a true null hypothesis.

Question 7

power of a test

Answer 7

Type II error. This is the failure to reject the null hypothesis when it is actually false.

The probability of correctly rejecting the null hypothesis when it is false. The power of a test is actually one minus the probability of making a Type II error, or 1 – P(Type II error).

The probability of rejecting the null when it is false (power of the test) equals one minus the probability of not rejecting the null when it is false (Type II error)

The power of the test for the competing test statistics may be useful in deciding which test statistic to use. Ordinarily, we wish to use the test statistic that provides the most powerful test among all possible tests.

Question 8

Confidence level

Answer 8

1 - Type I error. This is the rejection of the null hypothesis when it is actually true. or =α