A graphing calculator is recommended. A grassroots group opposed to a proposed i

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A graphing calculator is recommended.

A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are below. Using a 5% significance level, test the hypothesis that the three mean commuting mileages are the same. (Let 1 = Working-class, 2 = Professional (middle incomes), and 3 = Professional (wealthy).)

Part (a)

State the null hypothesis. Choose 1 or 2

1. H0: ?1 = ?2 = ?3H0:

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

Part (b)

State the alternative hypothesis. Choose 1 or 2

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

2. 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. Choose 1 2 3 4 5

1. F21, 23

2. F21, 2  

3.  F2, 23

4. F2, 21

5. F23, 21

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

____________

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

Explain what the p-value means for this problem. Choose answer

1. 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.

2.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.    

3.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.

4. 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.

Working-class Professional (middle incomes) Professional (wealthy) 16.9 16.0 8.4 26.2 16.7 5.4 48.7 21.8 4.4 9.2 7.1 11.7 65.2 8.6 10.6 46.5 1.9 28.3 19.0 5.9 14.8 50.4 13.0 8.9

Explanation / Answer

Part (a)

Correct option : 1. H0: ?1 = ?2 = ?3

Part (b)

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

Part (c)

df(num) = 2

Part (d)

df(denom) = 21

Part (e)

Correct option : 4. F2, 21

Now, we obtain the following ANOVA table after analysis:

Here , Test statistic = 9.06 (Two decimal places)

Here, P-value = 0.0015 ( Four decimal places)

The p-value means for this problem :

Correct option : 4. 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.

ANOVA Source of Variation SS df MS F P-value F crit Between Groups 3019.568 2 1509.784 9.05867 0.001457 3.4668 Within Groups 3500.013 21 166.6673 Total 6519.58 23

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