Question

A criminology student wishes to see if there is a relationship between the number of larceny crimes and the number of vandalism crimes on college campuses in southwestern Pennsylvania. The data are shown below. Number of larceny crimes: 24, 6, 16, 64, 10, 25, 35 No of vandalism crimes: 21, 3, 6, 15, 21, 61, 20 a. Find an appropriate measure to study the relationship between two variables and interpret it. Also explain that why you have been applied this method. b. In a painting competition, various entries are ranked by three judges. The results of Spearman's rank correlation for three possible pairs of judges are given below:- r12 = 0.81; r23 = 0.85; r13 = 0.83, i. Comment on the above results. ii. Which pair of judges do you think have the nearest approach and why?

          A criminology student wishes to see if there is a relationship between the number of larceny crimes and the number of vandalism crimes on college campuses in southwestern Pennsylvania. The data are shown below.

Number of larceny crimes: 24, 6, 16, 64, 10, 25, 35
No of vandalism crimes: 21, 3, 6, 15, 21, 61, 20

a. Find an appropriate measure to study the relationship between two variables and interpret it. Also explain that why you have been applied this method.
b. In a painting competition, various entries are ranked by three judges. The results of Spearman's rank correlation for three possible pairs of judges are given below:-
r12 = 0.81; r23 = 0.85; r13 = 0.83,
i. Comment on the above results.
ii. Which pair of judges do you think have the nearest approach and why?

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A criminology student wishes to see if there is a relationship between the number of larceny crimes and the number of vandalism crimes on college campuses in southwestern Pennsylvania. The data are shown below.

Number of larceny crimes: 24, 6, 16, 64, 10, 25, 35
No of vandalism crimes: 21, 3, 6, 15, 21, 61, 20

a. Find an appropriate measure to study the relationship between two variables and interpret it. Also explain that why you have been applied this method.
b. In a painting competition, various entries are ranked by three judges. The results of Spearman's rank correlation for three possible pairs of judges are given below:-
r12 = 0.81; r23 = 0.85; r13 = 0.83,
i. Comment on the above results.
ii. Which pair of judges do you think have the nearest approach and why?

Added by Taylor M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

07/10/2023

Step 1

Since we are dealing with two continuous variables, we can use the Pearson correlation coefficient (r) to measure the strength and direction of the linear relationship between them. To calculate the Pearson correlation coefficient, we will use the following Show more…

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A criminology student wishes to see if there is a relationship between the number of larceny crimes and the number of vandalism crimes on college campuses in southwestern Pennsylvania. The data are shown below. Number of larceny crimes: 24, 6, 16, 64, 10, 25, 35 No of vandalism crimes: 21, 3, 6, 15, 21, 61, 20 a. Find an appropriate measure to study the relationship between two variables and interpret it. Also explain that why you have been applied this method. b. In a painting competition, various entries are ranked by three judges. The results of Spearman's rank correlation for three possible pairs of judges are given below:- r12 = 0.81; r23 = 0.85; r13 = 0.83, i. Comment on the above results. ii. Which pair of judges do you think have the nearest approach and why?

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00:01 Hello student, appropriate measure for the study of relationship between two variables is pearson's correlation coefficient.

00:24 Given the values of x and y, we have calculated x minus x bar, y minus y bar, product of x minus x bar and y minus y bar, x minus x bar the whole square and y i minus y bar the whole square.

00:41 Now, the formula for pearson's correlation coefficient is r is equal to summation of x i minus x bar into y i minus y bar divided by square root of summation of x i minus x bar the whole square into summation of y i minus y bar the whole square.

01:02 Substituting values into the given equation, r is equal to minus 167 divided by square root of 2385 .4284 into 2186.

01:21 On simplifying, we will get the value of r as minus 0 .0731.

01:31 Hence, correlation coefficient between larceny crimes and vandalism crime is minus 0 .0731.

01:39 There is negligible negative correlation between these two crimes.

01:44 Method of correlation is used to determine the relationship between larceny crimes and vandalism crime because correlation coefficient measures the degree and direction of linear relationship between two variables.

01:58 It helps us to find out is there any relationship between two variables or not.

02:11 Correlation coefficient measures the degree and direction of linear relationship between two variables.

02:56 Now, in b part of the question, we have given that there are three judges for painting competition.

03:08 Spearman's rank correlation coefficient for different pairs is given as r12 is 0 .81, r23 is 0 .85, r13 is 0 .83...

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