Question

Tests in one teacher’s past classes have scores with a standard deviation equal to 14.1. One of their recent classes has 27 test scores with a standard deviation of 9.3. Use a 0.01 significance level to test the claim that this recent class has less variation than past classes. (15 points) a. Hypothesis (steps 1-3): b. Value of Test Statistic (steps 5-6): c. P-value (step 6): d. Decision (steps 4 and 7): e. Conclusion (step 8):

Answer 1

a) H₀: = 14.1

    H₁: < 14.1

b) The test statistic = (n - 1)s²/

                                    = 26 * (9.3)^2/(14.1)^2

                                    = 11.311

c) P-value = P( < 11.311)

                 = 1 - P( > 11.311)

                  = 1 - 0.9944

                  = 0.0056

d) Since the P-value is less than the significance level(0.0056 < 0.01), so we should reject the null hypothesis.

e) So at 0.01 significance level, there is sufficient evidence to support the claim that the recent class has less variation than past classes.