In June 2009, an onslaught of miserable weather in New England played havoc with people's plans and psyches. However, the dreary weather brought a quiet benefit to many city neighborhoods. Police reported that the weather was a key factor in reducing fatal and nondeadly shootings (The Boston Globe, July 3, 2009). For instance, it rained in Boston on 22 days in June, when 15 shootings occurred. In 2008, the city saw rain on only eight days, and 38 shootings occurred. The table below shows the number of rainy days and the number of shootings that occurred in June from 2005 to 2009. [You may find it useful to reference the t table.] Number of Rainy Days 7 Number of Shootings June 2005 31 June 2006 15 46 June 2007 10 29 June 2008 June 2009 38 22 15 SOURCE: The Boston Globe, July 3, 2009. B Click here for the Excel Data File a-1. Calculate the sample correlation coefficient. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal place Sample correlation coefficient a-2. Interpret the sample correlation coefficient between the number of rainy days and crime. OThe correlation coefficient indicates a positive linear relationship. O The correlation coefficient indicates a negative linear relationship. OThe correlation coefficient indicates no linear relationship. b. Specify the competing hypotheses in order to determine whether the population correlation coefficient between the number of rainy days and crime is negative. O Ho: Pxy 2 0; HA: Pxy < 0 OHọ: Pxy s 0; HA: Pxy > 0 OHo: Pxy = 0; HA: Pxy * 0 c-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
![In June 2009, an onslaught of miserable weather in New England played havoc with
people's plans and psyches. However, the dreary weather brought a quiet benefit to
many city neighborhoods. Police reported that the weather was a key factor in reducing
fatal and nondeadly shootings (The Boston Globe, July 3, 2009). For instance, it rained in
Boston on 22 days in June, when 15 shootings occurred. In 2008, the city saw rain on
only eight days, and 38 shootings occurred. The table below shows the number of rainy
days and the number of shootings that occurred in June from 2005 to 2009. [You may
find it useful to reference the t table.]
Number of Rainy
Number of
Shootings
Days
7
June 2005
31
June 2006
15
46
June 2007
June 2008
10
29
8
38
June 2009
22
15
SOURCE: The Boston Globe, July 3, 2009.
B Click here for the Excel Data File
a-1. Calculate the sample correlation coefficient. (Negative value should be indicated
by a minus sign. Round intermediate calculations to at least 4 decimal places and
final answers to 4 decimal places.)
Sample correlation coefficient
a-2. Interpret the sample correlation coefficient between the number of rainy days and
crime.
The correlation coefficient indicates a positive linear relationship.
The correlation coefficient indicates a negative linear relationship.
OThe correlation coefficient indicates no linear relationship.
b. Specify the competing hypotheses in order to determine whether the population
correlation coefficient between the number of rainy days and crime is negative.
OHo: Pxy 2 0; HẠ: Pxy < 0
OHo: Pxy s 0; HA: Pxy > 0
OHo: Pxy = 0; HA: Pxy = 0
c-1. Calculate the value of the test statistic. (Negative value should be indicated by a
minus sign. Round intermediate calculations to at least 4 decimal places and final
answer to 3 decimal places.)
Test statistic](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9141896-001f-4e78-8572-207ee29bce3c%2F0e9dbeba-6e69-484d-84fc-496499ac345b%2Fj79vmap_processed.jpeg&w=3840&q=75)
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