Question

A government aviation organization would like to determine if the average number of minutes that a plane departs late differs among airports in three major cities. The accompanying data were collected from randomly selected flights and indicate the number of minutes that each plane was behind schedule at its departure. Complete parts a and b. Click here to view the late departure data.

City 1 City 2 City 3

12 9 32

0 18    10

26    0 42

35    10    51

12 12    29

Click here to view a table of critical values for the studentized range. .

a. Perform a​ one-way ANOVA using α=0.05 to determine if there is a difference in the average lateness of the flights from these three airports.

Determine the null and alternative hypotheses.

H0​: ▼ μ1=μ2=μ3, μ1≠μ2≠μ3 , Not all μs are equal.

H1​:μ1≠μ2≠μ3, μ1=μ2=μ3, Not all μs are equal.

Determine the appropriate test statistic.

Fx= (Round to two decimal places as​ needed.)

Determine the​ p-value.

​p-value= ​(Round to three decimal places as​ needed.)

State the proper conclusion. ▼

(Reject/Do not reject) H0. There (is not/is) sufficient evidence to conclude that there is (no/a) difference in the average lateness of the flights from these three airports.

b. If​ warranted, perform a multiple comparison test to determine which pairs are different using α=0.05. Compare cities 1 and 2. Choose the correct answer below.

A. Since |x1−x2|<CR1,2​, conclude that the means for cities 1 and 2 are different.

B. Since |x1−x2|>CR1,2​, conclude that the means for cities 1 and 2 are are different.

C. Since |x1−x2|<CR1,2​, conclude that the means for cities 1 and 2 are not are not different.

D. Since |x1−x2>CR1,2​, conclude that the means for cities 1 and 2 are not different.

E. The multiple comparison test is not warranted.

Compare cities 1 and 3. Choose the correct answer below.

A. Since |x1−x3|> CR1,3​, conclude that the means for cities 1 and 3 are are different.

B. Since |x1−x3|>CR1,3​, conclude that the means for cities 1 and 3 are not different.

C. Since |x1−x3|<CR1,3​, conclude that the means for cities 1 and 3 are different.

D. Since |x1−x3|<CR1,3​, conclude that the means for cities 1 and 3 are not are not different.

E. The multiple comparison test is not warranted.

Compare cities 2 and 3. Choose the correct answer below.

A. Since |x2−x3| <CR2,3​, conclude that the means for cities 2 and 3 are not are not different.

B. Since |x2−x3| <CR2,3​, conclude that the means for cities 2 and 3 are different.

C. Since |x2−x3|> CR2,3​, conclude that the means for cities 2 and 3 are are different.

D. Since |x2−x3|>CR2,3​, conclude that the means for cities 2 and 3 are not different.

E. The multiple comparison test is not warranted.

Answer 1