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
19	29
20	19
15	22
16	31
24	19
20	28
11	23
16	39
18	29
20	19

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: 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    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 = 0H₀: 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

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

> Winter=scan("clipboard");Winter
Read 9 items
[1] 19 20 15 16 24 20 11 16 18
> Summer=scan("clipboard");Summer
Read 9 items
[1] 29 19 22 31 19 28 23 39 29
> wilcox.test(Winter, Summer, mu=0, alternative = "two.sided",conf.int = 0.95, exact = FALSE, correct = FALSE)

Wilcoxon rank sum test

data: Winter and Summer
W = 9, p-value = 0.005244
alternative hypothesis: true location shift is not equal to 0
95 percent confidence interval:
-13.000030 -3.000014
sample estimates:
difference in location
-8.999957

Answer:

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

Explanation:

The Wilcoxon Signed-Rank test is used to test the hypothesis whether the distribution of two populations is identical such that the difference of medians for two populations is zero.

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

Answer:

W = 9

p-value = 0.005244

Conclusion:

Since the p-value = 0.0055 is less than 0.05 at a 5% significance level, 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