Question

In this exercise involving paired differences, consider that it is reasonable to assume the populations being compared have approximately the same shape and that the distribution of paired differences is approximately symmetric.

Percents of on-time arrivals for flights in 2006 and 2007 were collected for 11 randomly selected airports. Suppose data for these airports follow.

Airport	Percent On-Time
	2006	2007
1	72.78	69.69
2	67.23	65.88
3	78.98	77.40
4	79.71	75.78
5	78.59	73.45
6	77.67	79.68
7	75.67	77.38
8	76.29	69.98
9	70.39	63.84
10	78.91	76.49
11	74.55	71.42

Use α = 0.05 to test the hypothesis that there is no difference between the median percent of on-time arrivals for the two years.

State the null and alternative hypotheses.

H₀: Median percent on-time in 2006 − Median percent on-time in 2007 > 0
H_a: Median percent on-time in 2006 − Median percent on-time in 2007 = 0

H₀: Median percent on-time in 2006 − Median percent on-time in 2007 ≤ 0
H_a: Median percent on-time in 2006 − Median percent on-time in 2007 > 0   

H₀: Median percent on-time in 2006 − Median percent on-time in 2007 ≠ 0
H_a: Median percent on-time in 2006 − Median percent on-time in 2007 = 0

H₀: Median percent on-time in 2006 − Median percent on-time in 2007 = 0
H_a: Median percent on-time in 2006 − Median percent on-time in 2007 ≠ 0

H₀: Median percent on-time in 2006 − Median percent on-time in 2007 ≥ 0
H_a: Median percent on-time in 2006 − Median percent on-time in 2007 < 0

Find the value of the test statistic.

T⁺ =

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the median percent of on-time arrivals for the two years.

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the median percent of on-time arrivals for the two years.    

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the median percent of on-time arrivals for the two years.

Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the median percent of on-time arrivals for the two years.

Answer 1

H₀: Median percent on-time in 2006 − Median percent on-time in 2007 = 0
H_a: Median percent on-time in 2006 − Median percent on-time in 2007 ≠ 0

T=max(W+,W-)       =

59

	mean =μ=n(n+1)/4 =		33
std dev=σ=√n(n+1)(2n+1)/24=			11.25
test statistic z score=(W-μ)/σ =			2.27
	p value =		0.0232

Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the median percent of on-time arrivals for the two years