Question

The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 1.7 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.025.

Answer 1

The statistical analysis suggests that there is sufficient evidence to reject the null hypothesis. The calculated p-value is less than the significance level of 0.025, indicating that the standard deviation of waiting times in the single waiting line scenario is indeed less than 1.7 minutes.

Step-by-step explanation:

In hypothesis testing, the null hypothesis (H₀) posits that there is no significant difference, while the alternative hypothesis (H₁) claims otherwise. In this case, the null hypothesis is that the standard deviation of waiting times in the single waiting line scenario is greater than or equal to 1.7 minutes. The alternative hypothesis is that the standard deviation is less than 1.7 minutes.

To conduct the hypothesis test, a sample of waiting times is collected, and the test statistic, typically a z-score, is calculated. The z-score measures how many standard deviations an observed data point is from the mean. The critical value or p-value is then compared to the predetermined significance level (α) to determine whether to reject the null hypothesis.

In our case, the p-value is calculated and compared to the significance level of 0.025. If the p-value is less than or equal to 0.025, we reject the null hypothesis in favor of the alternative hypothesis. This decision implies that there is enough evidence to support the claim that the standard deviation of waiting times in the single waiting line scenario is less than 1.7 minutes. It suggests that the efficiency gains achieved by having a single waiting line outweigh the potential increase in variability.

Answer 2

Based on the statistical analysis conducted at a significance level of 0.025, we reject the null hypothesis. There is sufficient evidence to support the claim that the standard deviation of waiting times for customers in the single waiting line is less than 1.7 minutes.

Explanation:

The null hypothesis (H0) in this case assumes that the standard deviation of waiting times in the single waiting line is greater than or equal to 1.7 minutes. The alternative hypothesis (H1) suggests that the standard deviation is less than 1.7 minutes. By conducting a hypothesis test with a significance level of 0.025, we evaluate whether there is enough evidence to reject the null hypothesis.

The test statistic is compared to a critical value or p-value to make this determination. If the test statistic falls in the critical region or if the p-value is less than 0.025, we reject the null hypothesis. In this context, rejecting the null hypothesis implies that there is a statistically significant difference in the standard deviation of waiting times between the single waiting line and separate waiting lines.

This conclusion is crucial for the bank, as it indicates that the use of a single waiting line feeding three teller windows leads to more consistent waiting times compared to the traditional approach of separate waiting lines. This information can inform operational decisions and potentially improve the overall customer experience at the bank.