Hypothesis Testing

p-value approach

*same first three steps* Step 4. Use the value of the test statistic to compute the p-value. Step 5. Reject H0 if p-value < α.

critical value approach

*same first three steps* Step 4: Determine the critical value and rejection rule. Step 5: Determine whether to reject H0.

Two procedures to make tests of hypothesis

1. The critical-value approach 2. The p-value approach

significance test

Applications of hypothesis testing that only control the Type I error

p-value approach to two-tailed hypothesis testing

Compute the p-value using the following three steps: 1. Compute the value of the test statistic z. 2. If z is in the upper tail (z > 0), find the area under the standard normal curve to the right of z. If z is in the lower tail (z < 0), find the area under the standard normal curve to the left of z. 3. Double the tail area obtained in step 2 to obtain the p -value. The rejection rule: Reject H0 if the p-value < α

Confidence Interval Approach to Two-Tailed Tests About a Population Mean

Select a simple random sample from the population and use the value of the sample mean to develop the confidence interval for the population mean α. If the confidence interval contains the hypothesized value H0, do not reject H0. Otherwise, reject H0. (Actually, H0 should be rejected if 0 happens to be equal to one of the end points of the confidence interval.)

steps of hypothesis testing

Step 1. Develop the null and alternative hypotheses. Step 2. Specify the level of significance (α) Step 3. Collect the sample data and compute the test statistic. Step 4. Use the level of significance to determine the critical value and the rejection rule. Step 5. Use the value of the test statistic and the rejection rule to determine whether to reject H0. Interpretation of results (what do the results mean)

level of significance

The probability of making a Type I error when the null hypothesis is true as an equality

critical value approach to two-tailed hypothesis testing

The rejection rule is: Reject H0 if z < -z α/2 or z > zα/2.

critical value

The value of the test statistic that established the boundary of the rejection region

type II error

accepting H0 when it is false.

hypothesis testing

can be used to determine whether a statement about the value of a population parameter should or should not be rejected

null hypothesis

denoted by H0 , is a tentative assumption about a population parameter

alternative hypothesis

denoted by Ha, is the opposite of what is stated in the null hypothesis

the test statistic

has a t distribution with n - 1 degrees of freedom.

p-value

is less than or equal to the level of significance, the value of the test statistic is in the rejection region.

type I error

rejecting H0 when it is true

p-value

the probability, computed using the test statistic, that measures the support (or lack of support) provided by the sample for the null hypothesis