Question

Police records show the following numbers of daily crime reports for a sample of days during the winter months and a sample of days during the summer months.

Winter	Summer
17	27
20	17
15	21
16	34
23	17
20	28
14	22
16	37
18	27
20	17

Use a 0.05 level of significance to determine whether there is a significant difference between the winter and summer months in terms of the number of crime reports.

State the null and alternative hypotheses.

H₀: Median number of daily crime reports for winter − Median number of daily crime reports for summer < 0
H_a: Median number of daily crime reports for winter − Median number of daily crime reports for summer = 0

H₀: The two populations of daily crime reports are identical.
H_a: The two populations of daily crime reports are not identical.    

H₀: Median number of daily crime reports for winter − Median number of daily crime reports for summer ≤ 0
H_a: Median number of daily crime reports for winter − Median number of daily crime reports for summer > 0

H₀: The two populations of daily crime reports are not identical.
H_a: The two populations of daily crime reports are identical.

H₀: Median number of daily crime reports for winter − Median number of daily crime reports for summer ≥ 0
H_a: Median number of daily crime reports for winter − Median number of daily crime reports for summer < 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 there is a significant difference between the winter and summer months in terms of the number of crime reports.

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.   

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.

Answer 1

H₀: The two populations of daily crime reports are identical.
H_a: The two populations of daily crime reports are not identical.    

wilcoxon sum rank test-

A	B	rank for sample 1	rank for sample 2
17	27	6.5	16.5
20	17	11	6.5
15	21	2	13
16	34	3.5	19
23	17	15	6.5
20	28	11	18
14	22	1	14
16	37	3.5	20
18	27	9	16.5
20	17	11	6.5

A      
sample size ,    n1 =    10
sum of ranks ,    R1 =    73.5
      
B      
sample size ,    n2 =    10
sum of ranks ,   R2 =    136.5
      
W=sum of ranks for smaller sample size =       73.5

p value exact=   0.019
Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.