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. Ha: ? ≠ 1.00 Ha: ? ≥ 1.00 Ha: ? = 1.00 Ha: ? < 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 hypothesis do 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.

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. Ha: ? ≠ 1.00 Ha: ? ≥ 1.00 Ha: ? = 1.00 Ha: ? < 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 hypothesis do 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 22SGR

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Related questions

Question

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 hypothesis do 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.