Suppose the mean wait-time for a telephone reservation agent...

Suppose the mean wait-time for a telephone reservation agent at a large airline is 43 seconds. A manager with the airline is concerned that business may be lost due to customers having to wait too long for an agent. To address this concern, the manager develops new airline reservation policies that are intended to reduce the amount of time an agent needs to spend with each customer. A random sample of 250 customers results in a sample mean wait-time of 42.3 seconds with a standard deviation of 4.2 seconds. Using an $\alpha=0.05$ level of significance, do you believe the new policies were effective? Do you think the results have any practical significance?

Key Concepts

Significance Level (?)

The significance level is the threshold used to decide whether the p-value indicates a statistically significant result. An ? of 0.05 means there is a 5% risk of rejecting the null hypothesis when it is actually true (Type I error). If the p-value is less than 0.05, it implies that the results are statistically significant and the evidence is strong enough to question the null hypothesis.

Hypothesis Testing

This concept involves formulating a null hypothesis and an alternative hypothesis to determine if there is sufficient evidence to support a claim about a population parameter based on sample data. In this case, the null hypothesis would state that the new policies have no effect on mean wait time, while the alternative hypothesis would suggest that the policies have reduced the mean wait time. The hypothesis testing framework provides a systematic method to decide whether to reject the null hypothesis based on the sample evidence.

Test Statistic and P-value

The test statistic is calculated from the sample data and reflects how far the sample mean deviates from the hypothesized population mean in terms of the standard error. The p-value, derived from this test statistic, quantifies the probability of obtaining results as extreme as the observed sample data if the null hypothesis were true. A small p-value indicates that the observed data is unlikely under the null hypothesis, leading to its rejection.

Statistical vs Practical Significance

Statistical significance refers to the likelihood that the observed effect in the sample is real and not due to random chance, as determined by the p-value relative to the significance level. Practical significance, on the other hand, considers whether the size of the effect is large enough to be of real-world value or importance. Even if a result is statistically significant, the actual improvement or reduction measured might be too small to have a meaningful impact on the organization’s operations or customer satisfaction.

Sample Size and Variability

The size of the sample and the variability of the data play a crucial role in hypothesis testing. A larger sample size tends to provide more reliable estimates of the population parameter by reducing the standard error, which can lead to the detection of even minor differences. However, it also necessitates care in evaluating whether a statistically significant difference is practically significant, since large samples can sometimes detect trivial differences that do not have substantial business or operational implications.

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