Question

The director of the IRS has been flooded with complaints that people must now wait more than 75 minutes before seeing an IRS representative. To determine the validity of these complaints, the IRS randomly selects 500 people entering the IRS offices across the country and records the times that they must wait before seeing an IRS representative. The average waiting time for the sample is 65 minutes with a standard deviation of 12 minutes. Are the complaints substantiated at alpha = 0.10? Show all work.

Answer 1

$H0: \mu = 75$

$H1: \mu > 75$

Under H0, the test statistic is

$t = \frac{\overline{x} -\mu }{s/\sqrt{n}} = \frac{65-75}{12/\sqrt{500}} = -18.63$

The P-Value is < .00001

since p value is less than significance level, Reject H0.

Hence the complaints are substantiated.