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)

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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