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	1
FL	17
GA	7
KY	5
LA	5
MS	4
NC	3
OK	2
SC	4
TN	0
TX	9
VA	0

Western State	Fatalities
AZ	6
CA	1
ID	2
MT	2
NM	2
NV	0
OR	2
UT	3
WA	0
WY	4

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: The two populations of lightning fatalities are identical.
H_a: The two populations of lightning fatalities are not 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 > 0H₀: 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 < 0H₀: The two populations of lightning fatalities are not identical.
H_a: The two populations of lightning fatalities are identical.

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?

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

Answer 1

For this we will use Mann-Whitney test

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

For identical population they should have no statistically significant difference between their medians

Mann-Whitney

Method

η₁: median of Fatalities SS

η₂: median of Fatalities WS

Difference: η₁ - η₂

Descriptive Statistics

Sample	N	Median
Fatalities SS	13	4
Fatalities WS	10	2

Estimation for Difference

Difference	CI for Difference	Achieved Confidence
2	(-1, 4)	95.62%

Test

Null hypothesis	H₀: η₁ - η₂ = 0
Alternative hypothesis	H₁: η₁ - η₂ ≠ 0

Method	W-Value	P-Value
Not adjusted for ties	182.00	0.114
Adjusted for ties	182.00	0.110

Conclusion

Since p-value is more than the level of significance (0.05), we fail to reject the null hypothesis

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