Question

1. For a particular scenario, we wish to test the hypothesis H₀ : μ = 14.9. For a sample of size 35, the sample mean X̄ is 12.7. The population standard deviation σ is known to be 8. Compute the value of the test statistic z_obs. (Express your answer as a decimal rounded to two decimal places.)

2. For a test of H₀ : μ = μ₀ vs. H₁ : μ ≠ μ₀, assume that the test statistic follows a t-distribution with 18 degrees of freedom. What is the critical value of the test if a 10% significance level is desired? (Express your answer as a positive decimal rounded to three decimal places.)

3. For a test of H₀ : μ = μ₀ vs. H₁ : μ ≠ μ₀, the value of the test statistic z _obs is -1.05. What is the p-value of the hypothesis test? (Express your answer as a decimal rounded to three decimal places.)

4. Which of the following is a valid alternative hypothesis for a one-sided hypothesis test about a population mean μ?

A. X̄ > 4.2

B. μ < 2.9

C. μ ≠ 5.4

D. μ = 3.8

5. Consider a test of H₀ : μ = μ₀ vs. H₀ : μ < μ₀. Suppose this test is based on a sample of size 8, that σ² is known, and that the underlying population is normal. If a 5% significance level is desired, what would be the rejection rule for this test?

Answer 1