A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose that the table below shows the results of a study.CNNFOXLocal4516721143371868563850602331513522 Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05. (Let 1 = CNN, 2 = FOX, and 3 = Local.)Part (a)State the null hypothesis.H0: ?1 = ?2 = ?3H0: At least two of the group means ?1, ?2, ?3 are not equal. Part (b)State the alternative hypothesis.Ha: At least two of the group means ?1, ?2, ?3 are not equal.Ha: ?1 = ?2 = ?3 Part (c)Enter an exact number as an integer, fraction, or decimal.df(num) = Part (d)Enter an exact number as an integer, fraction, or decimal.df(denom) = Part (e)State the distribution to use for the test.F16, 14F2, 14 F14, 2F14, 16F2, 16Part (f)What is the test statistic? (Round your answer to two decimal places.)Part (g)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 value of the test statistic will be equal to or less than the calculated value.If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value. If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.Part (h)Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value. Part (i)Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write appropriate conclusions.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)? = (ii) Decision:reject the null hypothesisdo not reject the null hypothesis (iii) Reason for decision:a.Since ? > p-value, we do not reject the null hypothesis.b.Since ? > p-value, we reject the null hypothesis. c. Since ? < p-value, we do not reject the null hypothesis.d. Since ? < p-value, we reject the null hypothesis.(iv) Conclusion:There is sufficient evidence to warrant a rejection of the claim that the mean times are the same.There is not sufficient evidence to warrant a rejection of the claim that the mean times are the same.

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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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A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose that the table below shows the results of a study.

CNN	FOX	Local
45	16	72
11	43	37
18	68	56
38	50	60
23	31	51
35	22

Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05. (Let 1 = CNN, 2 = FOX, and 3 = Local.)

Part (a)

State the null hypothesis.

H₀: ?₁ = ?₂ = ?₃

H₀: At least two of the group means ?₁, ?₂, ?₃ are not equal.
Part (b)

State the alternative hypothesis.

H_a: At least two of the group means ?₁, ?₂, ?₃ are not equal.

H_a: ?₁ = ?₂ = ?₃
Part (c)

Enter an exact number as an integer, fraction, or decimal.

df(num) =
Part (d)

Enter an exact number as an integer, fraction, or decimal.

df(denom) =
Part (e)

State the distribution to use for the test.

F_{16, 14}

F_{2, 14}

F_{14, 2}

F_{14, 16}

F_{2, 16}
Part (f)

What is the test statistic? (Round your answer to two decimal places.)
Part (g)

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 value of the test statistic will be equal to or less than the calculated value.If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value. If
H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
Part (h)

Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.
Part (i)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write appropriate conclusions.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)

? =

(ii) Decision:
reject the null hypothesis

do not reject the null hypothesis

(iii) Reason for decision:
a.Since ? > p-value, we do not reject the null hypothesis.

b.Since ? > p-value, we reject the null hypothesis.

c. Since ? < p-value, we do not reject the null hypothesis.

d. Since ? < p-value, we reject the null hypothesis.

(iv) Conclusion:
There is sufficient evidence to warrant a rejection of the claim that the mean times are the same.

There is not sufficient evidence to warrant a rejection of the claim that the mean times are the same.

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