Suppose that an accounting firm does a study to determine thetime needed to complete one person's tax forms. It randomly surveys150 people. The sample mean is 23.1 hours. There is a knownpopulation standard deviation of 6.4 hours. The populationdistribution is assumed to be normal.

NOTE: If you are using a Student's t-distribution, you mayassume that the underlying population is normally distributed. (Ingeneral, you must first prove that assumption, though.)

• Part (a)

  Find the following. (Enter exact numbers as integers, fractions, ordecimals.)(i)    

  x =

  
  
  (ii)    

  σ =

  
  
  (iii)    

  n =

• Part (b)

  In words, define the random variables X and X

  X is the number of tax forms that an accounting firmcompletes, and X is the mean number of tax forms that anaccounting firm completes.X is the number of tax formsthat an accounting firm completes, and X is the meannumber of tax forms that an accounting firmcompletes.    X is the time needed tocomplete one person's tax forms, and X is the mean timeneeded to complete tax forms from a sample of 150customers.X is the time needed to complete one person'stax forms, and X is the mean time needed to complete taxforms from a sample of 150 customers.

• Part (c)

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

  X ~

    ? Exp N B H U  ,  
  
  Explain your choice.

  The standard normal distribution should be used because the meanis given.The Student's t-distribution should be usedbecause the sample mean is smaller than30.    The standard normal distribution shouldbe used because the population standard deviation is known.TheStudent's t-distribution should be used because the samplestandard deviation is given.

• Part (d)

  Construct a 90% confidence interval for the population mean time tocomplete the tax forms.(i) State the confidence interval. (Roundyour 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 decimalplaces.)

• Part (e)

  If the firm wished to increase its level of confidence and keep theerror bound the same by taking another survey, what change shouldit make?

  It should increase the number of people surveyed.It shoulddecrease the number of people surveyed.    

• Part (f)

  If the firm did another survey, kept the error bound the same, andonly surveyed 49 people, what would happen to the level ofconfidence? Why?

  The level of confidence would be larger because we havecollected a smaller sample, obtaining less accurate information.Thelevel of confidence would be smaller because we have collected asmaller sample, obtaining less accurateinformation.    There would be no change.

• Part (g)

  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?

  The number of people surveyed would decrease because moreaccurate information requires a smaller sample.The number of peoplesurveyed would increase because more accurate information requiresa larger sample.    There would be nochange.