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.H_{0}: μ ≠ 1.00
H_{0}: μ = 1.00
H_{0}: μ < 1.00
H_{0}: μ ≥ 1.00
Part (b)
State the alternative hypothesis.H_{a}: μ ≠ 1.00
H_{a}: μ ≥ 1.00
H_{a}: μ < 1.00
H_{a}: 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.)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.)H_{0}
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.IfH_{0}
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. IfH_{0}
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.IfH_{0}
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:reject the null hypothesisdo 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. Since α > p-value, we reject the null hypothesis.Since α > p-value, we do not reject the null hypothesis.
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.
Dear student,
I am waiting for your feedback. I have given my 100% to solve your
queries. If you are satisfied by my given answer. Can you please
like it☺
Get Answers For Free
Most questions answered within 1 hours.