Question

Are Southern and Western states equally prone to fatal lightning strikes? Suppose the number of lightning strike fatalities over a 5-year period for Southern and Western states are shown as follows.

Southern State	Fatalities
AL	5
AR	2
FL	17
GA	7
KY	5
LA	5
MS	1
NC	3
OK	4
SC	1
TN	0
TX	8
VA	0

Western State	Fatalities
AZ	9
CA	2
ID	4
MT	4
NM	4
NV	0
OR	4
UT	3
WA	0
WY	1

Use α = 0.05 and test to determine whether the distribution of lightning fatalities is the same for these two regions.

State the null and alternative hypotheses.

H₀: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states ≥ 0
H_a: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states < 0

H₀: The two populations of lightning fatalities are identical.
H_a: The two populations of lightning fatalities are not identical.    

H₀: The two populations of lightning fatalities are not identical.
H_a: The two populations of lightning fatalities are identical.

H₀: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states ≤ 0
H_a: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states > 0

H₀: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states > 0
H_a: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states = 0

Find the value of the test statistic.

W =

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

p-value =

What is your conclusion?

Reject H₀. There is sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.

Do not reject H₀. There is not sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.    

Reject H₀. There is not sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.

Do not reject H₀. There is sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.

Answer 1

H₀: The two populations of lightning fatalities are identical.
H_a: The two populations of lightning fatalities are not identical.  

Applying WILCOXON RANK-SUM TEST :

sample size n1 =		13
sample size n2 =		10
Rank sum (R1)=		168
Rank sum (R2)=		108
test statistic =w1 =R1 =		168

mean =μ=n1(n1+n2+1)/2=		156
Variance σ2=n1n2(n1+n2+1)/12=		260.00
σ=√n1n2(n1+n2+1)/12=		16.125
z score =(w1-μ)/σ =		0.71
p value =	0.4778		(from excel:2*normsdist(-0.71)

Do not reject H₀. There is not sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.