The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared. He would like to add an additional billing counter if the variance exceeds the cut-off. He checks the recent sample data. For a random sample of 24 customer waiting times, he arrives at a sample variance of 3.8 minutes-squared. The manager assumes the waiting times to be normally distributed. Which of the following would be null and the alternate hypothesis to test if the cut-off is surpassed? A) Η₀: σ² ≤ 2.3, Η_A: σ² 2.3. B) Η₀: σ² = 2.3, Η_A: σ² ≠ 2.3. C) Η₀: σ² ≥2.3, Η_A: σ²

Question

The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared. He would like to add an additional billing counter if the variance exceeds the cut-off. He checks the recent sample data. For a random sample of 24 customer waiting times, he arrives at a sample variance of 3.8 minutes-squared. The manager assumes the waiting times to be normally distributed. Which of the following would be null and the alternate hypothesis to test if the cut-off is surpassed? A) Η₀: σ² ≤ 2.3, Η_A: σ² > 2.3. B) Η₀: σ² = 2.3, Η_A: σ² ≠ 2.3. C) Η₀: σ² ≥2.3, Η_A: σ² < 2.3. D) Η₀: σ² < 2.3, Η_A: σ² ≥ 2.3.

Quizplus · Accepted Answer

The null hypothesis (H0) is a statement of no effect or no difference, and it often represents a statement of equality (e.g., ≤ or =). The alternate hypothesis (H1 or Ha) is what one might want to prove to be true, representing a statement of inequality (e.g., >, ≠, <). In this scenario, the manager wants to test if the variance exceeds 2.3 minutes-squared. Therefore, the null hypothesis should state that the population variance is less than or equal to 2.3 minutes-squared (σ^2 ≤ 2.3), and the alternate hypothesis should state that the population variance is greater than 2.3 minutes-squared (σ^2 > 2.3), which matches option A.

The Manager of a Video Library Would Like the Variance