Explain what a critical value is, and explain how it is used to test a hypothesis.
Exercises for Section 9.2
CONCEPTS
9.14 Explain what a critical value is, and explain how it is used to test a hypothesis.
9.15 Explain what a p-value is, and explain how it is used to test a hypothesis.
METHODS AND APPLICATIONS
In Exercises 9.16 through 9.22 we consider using a random sample of 100 measurements to test H0: μ = 80 versus Ha: μ > 80. If and σ = 20:
9.16 Calculate the value of the test statistic z.
9.17 Use a critical value to test H0 versus Ha by setting α equal to .10.
9.18 Use a critical value to test H0 versus Ha by setting α equal to .05.
9.19 Use a critical value to test H0 versus Ha by setting α equal to .01.
9.20 Use a critical value to test H0 versus Ha by setting α equal to .001.
9.21 Calculate the p-value and use it to test H0 versus Ha at each of α = .10, .05, .01, and .001.
9.22 How much evidence is there that H0: μ = 80 is false and Ha: μ > 80 is true?
In Exercises 9.23 through 9.29 we consider using a random sample of 49 measurements to test H0: μ = 20 versus Ha: μ < 20. If and σ = 7:
9.23 Calculate the value of the test statistic z.
9.24 Use a critical value to test H0 versus Ha by setting α equal to .10.
9.25 Use a critical value to test H0 versus Ha by setting α equal to .05.
9.26 Use a critical value to test H0 versus Ha by setting α equal to .01.
9.27 Use a critical value to test H0 versus Ha by setting α equal to .001.
9.28 Calculate the p-value and use it to test H0 versus Ha at each of α = .10, .05, .01, and .001.
9.29 How much evidence is there that H0: μ = 20 is false and Ha: μ < 20 is true?
In Exercises 9.30 through 9.36 we consider using a random sample of n = 81 measurements to test H0: μ = 40 versus Ha: μ ≠ 40. If and σ = 18:
9.30 Calculate the value of the test statistic z.
9.31 Use critical values to test H0 versus Ha by setting α equal to .10.
9.32 Use critical values to test H0 versus Ha by setting α equal to .05.
9.33 Use critical values to test H0 versus Ha by setting α equal to .01.
9.34 Use critical values to test H0 versus Ha by setting α equal to .001.
9.35 Calculate the p-value and use it to test H0 versus Ha at each of α = .10, .05, .01, and .001.
9.36 How much evidence is there that H0: μ = 40 is false and Ha: μ ≠ 40 is true?