Question

The Internal Revenue Service (IRS) provides a toll-free help line for tax payers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with tax payer calls and has redesigned its phone service as well as posting answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). 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. Suppose you select a sample of 50 callers after the new phone service has been implemented; the sample results show a mean waiting time of 10 minutes before an IRS employee comes on line. Based upon data from past years, you decide it is reasonable to assume that the standard deviation of waiting times is 8 minutes Using your sample results, can you conclude that the actual mean waiting time turned out to be significantly less than the 12 minute claim made by the taxpayer advocate? Use a.05 Select your answer- Yes No

Answer 1

null hypothesis: Alternate Hypothesis 12 12 for 0.05 level with left tailed test, critical value of z Decision rule 1.6449 reject Ho if test statistic z<-1.645 population mean mean sample size population std deviation 12 10.000 50 8.000 μ: X- 1.131 test statistic z (X-μ)/σ,- Ξ

here as test statisitc is less than critical value ; we rreject null hpothesis

hence Yes