Question

n-Class Exercise 1 Instructions: Submit your work through Blackboard by the due date. Late submissions are not allowed. You can take photos of or scan your solutions Calculate or write the formulas for each test statistic and p-value for each hypothesis test question (questions 7-10). It is true you will never have to calculate these in real life, however, you should know what Megastat, or any other statistical software, is calculating. 1) According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A consumer watchdog agency selects a random sample of 40 taxpayers. a) What is the standard error of the mean in this example? b) What is the likelihood the sample mean is greater than 320 minutes? c) What is the likelihood the sample mean is greater than 350 minutes? 99 Words English (US

Answer 1

1)

Mean=330

Standard deviation= 80

Number of samples(n)= 40

a) Standard error: $s= \sigma /\sqrt{n}=80/\sqrt{40}=12.64911$

b) P(Sample mean >320)

$Z=\frac{x-\mu }{s}=\frac{320-330}{12.64911}=-0.790569$

Using normal distribution table: P(Z>-0.790569)= 0.7854

So, P(Sample mean > 320)= 07854

c) P(Sample mean > 350)

$Z=\frac{x-\mu }{s}=\frac{350-330}{12.64911}=1.58114$

Using normal distribution table: P(Z>1.58114)= 0.0569

So, P(Sample mean > 350)= 0.0569