Question

Is there evidence of a difference in the variability of the waiting time between the two banks? (Use α = 0.01.) Determine the hypotheses. Choose the correct answer below.

a. Null Hypothesis:
b. Alternative Hypothesis:

Answer 1

To determine if there's a difference in waiting time variability between two banks, set up hypotheses (σ1² = σ2² for null and σ1² ≠ σ2² for alternative) and compare the p-value to α = 0.01 to decide if there is sufficient evidence to reject or not reject the null hypothesis.

Step-by-step explanation:

Understanding Hypothesis Testing for Variability of Waiting Time

To determine if there is a difference in the variability of waiting times between two banks, one needs to perform hypothesis testing. The hypotheses for this situation comparing variances would typically be set up as follows:

• Null Hypothesis (H0): There is no difference in the variability of waiting times between the two banks. In statistical terms, σ1² = σ2².
• Alternative Hypothesis (Ha): There is a difference in the variability of waiting times between the two banks, which means σ1² ≠ σ2².

Using an alpha level (α) of 0.01, we compare the p-value obtained from the test to this significance level to make a decision:

• If p-value < α: Reject the null hypothesis, indicating there is enough evidence of a difference in variability.
• If p-value ≥ α: Do not reject the null hypothesis, indicating there is not enough evidence to support the claim of different variabilities.

The information provided suggests making a decision based on comparing alpha to the p-value. Without the specific p-value, the exact decision can't be determined, but the process to decide has been given.