Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys175people. The sample mean is22.6hours. There is a known population standard deviation of7.0hours. The population distribution is assumed to be normal.

NOTE: If you are using a Student'st-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

• Part (a)
• Find the following. (Enter exact numbers as integers, fractions, or decimals.)
• (i)x=
• (ii)=
• (iii)n=
• Part (b)
• In words, define the random variablesXandX

a) Xis the time needed to complete one person's tax forms, andXis the mean time needed to complete tax forms from a sample of 175 customers.

b) Xis the number of tax forms that an accounting firm completes, andXis the mean number of tax forms that an accounting firm completes.

c) Xis the number of tax forms that an accounting firm completes, andXis the mean number of tax forms that an accounting firm completes.

d) Xis the time needed to complete one person's tax forms, andXis the mean time needed to complete tax forms from a sample of 175 customers.

• Part (c)
• Which distribution should you use for this problem? (Round your answers to two decimal places.)
• X~____(_____,______)
• Explain your choice.

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

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

c) The Student'st-distribution should be used because the sample standard deviation is given.

d) The Student'st-distribution should be used because the sample mean is smaller than 30.

• Part (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.)
• a/2 = ____ C.L.= ______ a/2=____
• (iii) Calculate the error bound. (Round your answer to two decimal places.)
• Part (e) Multiple choice
• If the firm wished to increase its level of confidence and keep the error bound the same by taking another survey, what change should it make?

a) It should increase the number of people surveyed.

b) It should decrease the number of people surveyed.

• Part (f) Multiple choice
• If the firm did another survey, kept the error bound the same, and only surveyed 49 people, what would happen to the level of confidence? Why?

a) The level of confidence would be larger because we have collected a smaller sample, obtaining less accurate information.

b) The level of confidence would be smaller because we have collected a smaller sample, obtaining less accurate information.

c) There would be no change.

• Part (g) Multiple choice
• Suppose that the firm decided that it needed to be at least 96% confident of the population mean length of time to within one hour. How would the number of people the firm surveys change? Why?

a) The number of people surveyed would decrease because more accurate information requires a smaller sample.

b) The number of people surveyed would increase because more accurate information requires a larger sample.

c) There would be no change.