Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that the table below shows the results of a study.WhiteBlackHispanicAsian54898133255542416 67Assume 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 = White, 2 = Black, 3 = Hispanic, and 4 = Asian.)Part (a)State the null hypothesis.H0: ?1 = ?2 = ?3 = ?4H0: At least two of the group means ?1, ?2, ?3, ?4, are not equal. 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.F3, 18F15, 3 F3, 15F18, 15F15, 18Part (f) Part (g)What is the p-value? (Round your answer to four decimal places.)Explain what the p-value means for this problem.If H0is 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 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 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: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 mean numbers of times per month a person eats out are the same for whites, blacks, Hispanics, and Asians.There is not sufficient evidence to warrant a rejection that the mean numbers of times per month a person eats out are the same for whites, blacks, Hispanics, and Asians.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that the table below shows the results of a study.

White	Black	Hispanic	Asian
5	4	8	9
8	1	3	3
2	5	5	5
4	2	4	1
6		6	7

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 = White, 2 = Black, 3 = Hispanic, and 4 = Asian.)

Part (a)

State the null hypothesis.

H₀: ?₁ = ?₂ = ?₃ = ?₄

H₀: At least two of the group means ?₁, ?₂, ?₃, ?₄, are not equal.
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_{3, 18}

F_{15, 3}

F_{3, 15}

F_{18, 15}

F_{15, 18}
Part (f)
Part (g)

What is the p-value? (Round your answer to four decimal places.)

Explain what the p-value means for this problem.
If H₀is 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 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 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:
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 mean numbers of times per month a person eats out are the same for whites, blacks, Hispanics, and Asians.

There is not sufficient evidence to warrant a rejection that the mean numbers of times per month a person eats out are the same for whites, blacks, Hispanics, and Asians.