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 $0.97 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: ? = 1.00H0: ? < 1.00 H0: ? ≠ 1.00H0: ? ≥ 1.00Part (b)State the alternative hypothesis.Ha: ? ≠ 1.00Ha: ? ≥ 1.00 Ha: ? = 1.00Ha: ? < 1.00Part (c)In words, state what your random variable X represents.X represents the cost of a daily newspaper.X represents the number of cities that publish daily newspapers. X represents how much the cost of a daily newspaper varies from the average cost of all daily newspapers.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 ~ , 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.) = 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 $0.97 or less OR $1.03 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 not $0.97 or less OR $1.03 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 $0.97 or less OR $1.03 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 $0.97 or less OR $1.03 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:? = (ii) Decision:reject the null hypothesisdo not reject the null hypothesis (iii) Reason for decision:Since ? > p-value, we reject the null hypothesis.Since ? < p-value, we reject the null hypothesis. Since ? > p-value, we do not reject the null hypothesis.Since ? < 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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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 $0.97 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: ? = 1.00
  
  H₀: ? < 1.00
  
  H₀: ? ≠ 1.00
  
  H₀: ? ≥ 1.00
- Part (b)
  
  State the alternative hypothesis.
  
  H_a: ? ≠ 1.00
  
  H_a: ? ≥ 1.00
  
  H_a: ? = 1.00
  
  H_a: ? < 1.00
- Part (c)
  
  In words, state what your random variable X represents.
  X represents the cost of a daily newspaper.X represents the number of cities that publish daily newspapers. X represents how much the cost of a daily newspaper varies from the average cost of all daily newspapers.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 ~
  
  ,
- 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.)
  =
- 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 $0.97 or less OR $1.03 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 not $0.97 or less OR $1.03 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 $0.97 or less OR $1.03 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 $0.97 or less OR $1.03 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:
  ? =
  
  (ii) Decision:
  reject the null hypothesisdo not reject the null hypothesis
  
  (iii) Reason for decision:
  Since ? > p-value, we reject the null hypothesis.Since ? < p-value, we reject the null hypothesis.    Since ? > p-value, we do not reject the null hypothesis.Since ? < 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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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