Question

The cost of a daily newspaper varies from city to city. However, the variation among prices remains steady with a population standard deviation of $0.20. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. Thirteen costs yield a mean cost of $0.95 with a standard deviation of $0.18. Do the data support the claim at the 1% level?

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

• Part (a)

  State the null hypothesis.

  H₀: μ ≠ 1.00

  H₀: μ = 1.00

       

  H₀: μ < 1.00

  H₀: μ ≥ 1.00

• Part (b)

  State the alternative hypothesis.

  H_a: μ ≠ 1.00

  H_a: μ ≥ 1.00

       

  H_a: μ < 1.00

  H_a: μ = 1.00

• Part (c)

  In words, state what your random variable X represents.

  X represents how much the cost of a daily newspaper varies from the average cost of all daily newspapers.X represents the number of cities that publish daily newspapers.     X represents the cost of a daily newspaper.X represents the average cost of a daily newspaper.

• Part (d)

  State the distribution to use for the test. (Round your answers to four decimal places.)
  X ~  ? G B Exp N U   ,  

• Part (e)

  What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)
  ? z t =

• Part (f)

  What is the p-value? (Round your answer to four decimal places.)
  
  
  Explain what the p-value means for this problem.If

  H₀

  is false, then there is a chance equal to the p-value that the average cost of a daily newspaper is not $0.95 or less OR $1.05 or more.If

  H₀

  is true, then there is a chance equal to the p-value that the average cost of a daily newspaper is not $0.95 or less OR $1.05 or more.      If

  H₀

  is false, then there is a chance equal to the p-value that the average cost of a daily newspaper is $0.95 or less OR $1.05 or more.If

  H₀

  is true, then there is a chance equal to the p-value that the average cost of a daily newspaper is $0.95 or less OR $1.05 or more.

• Part (g)

  Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. (Upload your file below.)

• Part (h)

  Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.(i) Alpha:
  α =  
  
  (ii) Decision:

  reject the null hypothesisdo not reject the null hypothesis     

  
  (iii) Reason for decision:

  Since α < p-value, we reject the null hypothesis.Since α < p-value, we do not reject the null hypothesis.     Since α > p-value, we reject the null hypothesis.Since α > p-value, we do not reject the null hypothesis.

  
  (iv) Conclusion:

  There is sufficient evidence to warrant a rejection of the claim that the average cost of a daily newspaper is equal to $1.00.There is not sufficient evidence to warrant a rejection of the claim that the the average cost of a daily newspaper is equal to $1.00.    

Answer 1

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