The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posted answers to frequently asked questions on its website.

According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of 12 minutes before being able to talk to an IRS employee. You suspect that the report is too pessimistic and that the new phone service is in fact more efficient.

The hypothesis test is:

H₀: =12 v.s. H₁:<12

Based upon the data from past years, you decide that it is reasonable to assume that the standard deviation of waiting time is 8 minutes. You also decide that you are going to collect a sample of 49 individuals. Assume that a sample size of 49 is large enough for the Central Limit Theorem to apply.

Suppose that, before collecting your sample, you settle in the following decision rule: "I will reject the null if the average waiting time in my sample of 49 callers is less than 9.5 minutes". What is the significance level implicit in that decision rule?

(Recall that the significance level is the probability of rejecting the null when the null is true).

Enter your answer rounded to three decimal places.