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