The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers

Question

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 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 14 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 12 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 10 minutes. Use =0.05

What is the p-value (to 4 decimals)?

(I've worked this problem out and each time I've gotten a z-score of -1.414 which equates to a p-value of 0.0787, but this is NOT the right answer according to my HW software so I think I'm doing something wrong.)

Explanation / Answer

Here you can take the z-score for 2 decimals which is -1.41.

· Now if it is one-tailed test then we get the p-value as follows:

P ( z < -1.41 ) = 0.0793

P-value = 0.0793

We get this value by using excel function or by using normal distribution table.

Excel function: =normsdist(-1.41)

· Now if it is two-tailed test then we get the p-value as follows:

2* P ( z < -1.41 ) = 2* 0.0793

                             = 0.1586

P-value = 0.1586

We get this value by using excel function or by using normal distribution table.

Excel function: =2*normsdist(-1.41)

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