The following table lists the number of pages in four different types of magazines.Home decoratingNewsHealthComputer17087821002859215013416012285982031039920519610196145Using a significance level of 5%, test the hypothesis that the four magazine types have the same average length. (Let 1 = Home decorating, 2 = News, 3 = Health and 4 = Computer.)Part (a)State the null hypothesis.H0: At least two of the group means ?1, ?2, ?3, ?4 are not equal.H0: ?1 = ?2 = ?3 = ?4 Part (b)State the alternative hypothesis.Ha: At least two of the group means ?1, ?2, ?3, ?4 are not equal.Ha: ?1 = ?2 = ?3 = ?4 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, 3F3, 16 F3, 19F19, 16F16, 19Part (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 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. 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 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.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) 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:Since ? < p-value, we do not 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 reject the null hypothesis.(iv) Conclusion:There is sufficient evidence to warrant a rejection that the four magazine types have the same average length.There is not sufficient evidence to warrant a rejection that the four magazine type have the same average length.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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Question

The following table lists the number of pages in four different types of magazines.

Home decorating	News	Health	Computer
170	87	82	100
285	92	150	134
160	122	85	98
203	103	99	205
196	101	96	145

Using a significance level of 5%, test the hypothesis that the four magazine types have the same average length. (Let 1 = Home decorating, 2 = News, 3 = Health and 4 = Computer.)

Part (a)

State the null hypothesis.

H₀: At least two of the group means ?₁, ?₂, ?₃, ?₄ are not equal.

H₀: ?₁ = ?₂ = ?₃ = ?₄
Part (b)

State the alternative hypothesis.

H_a: At least two of the group means ?₁, ?₂, ?₃, ?₄ are not equal.

H_a: ?₁ = ?₂ = ?₃ = ?₄
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, 3}

F_{3, 16}

F_{3, 19}

F_{19, 16}

F_{16, 19}
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 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. 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 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.
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) 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:
Since ? < p-value, we do not 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 reject the null hypothesis.

(iv) Conclusion:
There is sufficient evidence to warrant a rejection that the four magazine types have the same average length.

There is not sufficient evidence to warrant a rejection that the four magazine type have the same average length.

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