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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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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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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