Answered: Police records show the following…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	21
18	33
22	19
20	27
13	24
18	39
17	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 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: 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 < 0

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

(A) 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.

(B) 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.

(D) 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.

(D) 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.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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