Question

PROBLEM: Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 200 people. The sample mean is 23.1 hours. There is a known population standard deviation of 6.2 hours. The population distribution is assumed to be normal.

a) Find the following. (Enter exact numbers as integers, fractions, or decimals.)

x-bar = ______

σ = ______

n = _______

b) In words, define the random variables X and X-bar

X-bar is the time needed to complete one person's tax forms, and X is the mean time needed to complete tax forms from a sample of 200 customers.

X is the number of tax forms that an accounting firm completes, and X-bar is the mean number of tax forms that an accounting firm completes.

X is the time needed to complete one person's tax forms, and X-bar is the mean time needed to complete tax forms from a sample of 200 customers.

X-bar is the number of tax forms that an accounting firm completes, and X is the mean number of tax forms that an accounting firm completes.

c) Which distribution should you use for this problem? (Round your answers to two decimal places.)

X-bar ~ ____ (___,___)

Explain your choice.

The standard normal distribution should be used because the mean is given.

The standard normal distribution should be used because the population standard deviation is known.

The Student's t-distribution should be used because the sample standard deviation is given.

The Student's t-distribution should be used because the sample mean is smaller than 30.

d) Construct a 90% confidence interval for the population mean time to complete the tax forms.

(i) State the confidence interval. (Round your answers to two decimal places.)

(____,____)

(ii) Sketch the graph. (Round your answers to two decimal places.)

  

^ ____ ^____

(iii)  Calculate the error bound. (Round your answer to two decimal places.)

  

Answer 1

a)

b)

X is the time needed to complete one person's tax forms, and X-bar is the mean time needed to complete tax forms from a sample of 200 customers.

c)

We have

So,

The standard normal distribution should be used because the population standard deviation is known.

d)

(i)

(ii)

(iii)

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