Question

The cost of a daily newspaper varies from city to city. However, the variation among prices...

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.

    Ha: μ ≠ 1.00

    Ha: μ ≥ 1.00

         

    Ha: μ < 1.00

    Ha: 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.    

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