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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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