Question

# PROBLEM: Suppose that an accounting firm does a study to determine the time needed to complete...

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 ~ ____ (___,___)

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.)

(____,____)

^ ____ ^____

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

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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