Question

When lights are relayed, do two of the worst alports experience delays of the same length Suppose the delay times in minutes for seven recent, randomly selected delayed flights departing from ach of these airports are as follows Airport 1 Airport Use the MWW test to determine if there is a si nce length of night delays for these two airport 005 State the land native potheses OR: Median delay time for a porti Madanelay time for a t 20 Median delay time for a t Median delay time for sport 20 O No: The two populations of hight delsys are not entical The op tions of light dels edentical OH: The two populations of light dels are identical The two populations of it as a national O : Modian delay time for airport 1 Medan delay time for arport 2 0 Heden delay time for airport Medan delay time for art 2 - 0 O No Median delay time for airport 1 - Median delay time for airport 250 No: Modian delay tiene los aportt Median delay time for sport 2 > 0 Find the value of the test statistic

Answer 1

First, we put both samples together and organize it in ascending order, which is shown in the table below:

Sample	Value
1	23
2	33
2	37
1	38
1	41
1	45
2	48
2	52
1	57
1	69
2	74
2	82
1	95
2	103

Now, that the values that are in ascending order are assigned ranks to them, taking care of assigning the average rank to values with rank ties

Sample	Value	Rank	Rank (Adjusted for ties)
1	23	1	1
2	33	2	2
2	37	3	3
1	38	4	4
1	41	5	5
1	45	6	6
2	48	7	7
2	52	8	8
1	57	9	9
1	69	10	10
2	74	11	11
2	82	12	12
1	95	13	13
2	103	14	14

The sum of ranks for sample 1 is:

R1​=1+4+5+6+9+10+13=48

and the sum of ranks of sample 2 is:

R2​=2+3+7+8+11+12+14=57

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0​: Median (Difference) = 0 i.e Median delay time for airport 1 = Median delay time for airport 2

Ha​: Median (Difference) $\ne̸​=$ 0 i.e Median delay time for airport 1 $\ne̸​=$  Median delay time for airport 2

Test statistic W : 20

p-value : 0.620047

null hypothesis   μ0=μ0= 0.0

alternative hypothesis: two sided,  

Since p value=0.620047 > 0.05. there is not enough evidence to claim that the population median of differences is different than 0, at the 0.05 significance level.

> A <- c(69, 95, 41, 38, 57, 23, 45) B <- c(103, 33, 37, 82, 74, 48, 52) V V V > wilcox.test(A, B, paired = FALSE, alternative = "two.sided", mu = 0.0, exact = TRUE, correct = TRUE, conf. int = TRUE, conf.level = 0.95) + Wilcoxon rank sum test data: A and B W = 20, p-value = 0.62 alternative hypothesis: true location shift is not equal to O 95 per cent confidence interval: -41 21 sample estimates: difference in location -8