1. Explain what a critical value is, and explain how it is used to test a hypothesis.
2. Explain what a p-value is, and explain how it is used to test a hypothesis.
METHODS AND APPLICATIONS
3. Suppose that we wish to test H0: m = 80 versus Ha: m > 80, where s is known to equal 20. Also, suppose that a sample of n = 100 measurements randomly selected from the population has a mean of x = 85.
a. Calculate the value of the test statistic z.
b. By comparing z with a critical value, test H0 versus Ha at a = .05.
c. Calculate the p-value for testing H0 versus Ha.
d. Use the p-value to test H0 versus Ha at each of a = .10, .05, .01, and .001.
e. How much evidence is there that H0: m = 80 is false and Ha: m > 80 is true?