Question

Lyme disease is an inflammatory disease that results in a skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning deaths for a rural county. Complete parts (a) through (c) below. Click here to view the table of Lyme disease and drowning deaths Click here to view the critical values table (a) Draw a scatter diagram of the data. Let the number of reported cases of Lyme disease be the explanatory variable Choose the correct graph below. ОА A Drowning 20- OB Arown 20 Ос. A Drowning 20 OD A Drowning 20- @ 30 Lyme Disease Lyne Dee (1) Determine the linear correlation coefficient between Lyme disease and drowning deaths. The Inear correlation coefficient between Lyme disease and drowning deaths isr- (Round to three decimal places as needed.) (c) Does a linear relation exist between the number of reported cases of Lyme disease and the number of drowning deaths? Do you believe that an increase of Lyme disease causes an increase in drowning deaths? What is a likey lurking variable between cases of Lyme disease and drowning deaths? The variables Lyme disease and drowning deaths are associated because is and the absolute value of the correlation coefficient, is than the critical

Answer 1

a)

Ов. а 20 С (с 0 30

b)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	82.00	45.00	453.67	246.25	323.50
mean	6.83	3.75	SSxx	SSyy	SSxy

Sample size,   n =   12      
here, x̅ = Σx / n=   6.833          
ȳ = Σy/n =   3.750          
SSxx =    Σ(x-x̅)² =    453.6667      
SSxy=   Σ(x-x̅)(y-ȳ) =   323.5      
              
estimated slope , ß1 = SSxy/SSxx =   323.5/453.6667=   0.7131      
intercept,ß0 = y̅-ß1* x̄ =   3.75- (0.7131 )*6.8333=   -1.1227      
              
Regression line is, Ŷ=   -1.12   + (   0.713   )*x
              
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    15.5691      
std error ,Se =    √(SSE/(n-2)) =    1.2478      
              
correlation coefficient ,    r = SSxy/√(SSx.SSy) =   0.968   

c)

Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   12  
alpha,α =    0.05  
correlation , r=   0.9679  
t-test statistic = r*√(n-2)/√(1-r²) =        12.1724
DF=n-2 =   10     

critical t-value =    2.2281  

Decison:   t sttas > critical , So, Reject Ho  

O A. An increase in Lyme disease does not cause an increase in drowning deaths. The temperature and time of year are likely lurking variables.

Please let me know in case of any doubt.

Thanks in advance!

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