Question

DETAILSIDCOLLABSTAT2 8.HW.006.

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PRACTICE ANOTHER

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 average is 23.7 hours. There is a known population standard deviation of 6.0 hours. The population distribution is assumed to be normal.

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

• Part (a)

  (i)    

  x = 

  
  
  (ii)    

  𝜎 = 

  
  
  (iii)    

  𝜎 _x = 

   (rounded to three decimal places)
  
  (iv)    

  n = 

  
  
  (v)    

  n − 1 = 

• Part (b)

• Part (c)

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

  X ~

    
    ,  
  
  
  Explain your choice.

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

• Part (d)

  Construct a 90% confidence interval for the population average time to complete the tax forms.

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

    ,  
  
  
  (ii) Sketch the graph.

  

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