Question

Cigarette Smoking and Cancer Death Rates Deaths per year per 100,000 people Cigarettes Bladder per person Massachusetts (a) Draw a scatter diagram of cigarettes smoked versus death rate from bladder cancer 5.

Answer 1

a)

Scatterplot 1000 4000 0 2000 3000 5000

b)

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
2860	4.46	93373.898	0.173	127.249
2010	3.08	296402.469	0.928	524.596
2791	4.75	55966.041	0.499	167.121
2618	4.09	4041.327	0.002	2.952
2212	4.23	117257.33	0.035	-63.84
2184	2.91	137217.33	1.285	419.91
2344	2.86	44280.18	1.401	249.06
2692	4.69	18925.8980	0.4179	88.9301
2206	3.72	121402.469	0.105	112.742
2914	5.3	129291.612	1.579	451.776
3034	3.46	229988.755	0.341	-279.864
4240	6.54	2841151.041	6.232	4207.909
1400	3.31	1332705.327	0.538	846.856
2257	3.21	88463.755	0.695	247.928

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	35762	56.61	5510467.429	14.23	7103.31857
mean	2554.43	4.04	SSxx	SSyy	SSxy

sample size ,   n =   14          
here, x̅ = Σx / n=   2554.43   ,     ȳ = Σy/n =   4.04  
                  
SSxx =    Σ(x-x̅)² =    5510467.4286          
SSxy=   Σ(x-x̅)(y-ȳ) =   7103.3          
                  
estimated slope , ß1 = SSxy/SSxx =   7103.3   /   5510467.429   =   0.0013
                  
intercept,   ß0 = y̅-ß1* x̄ =   0.7508          
                  
so, regression line is   Ŷ =   0.7508   +   0.0013   *x

c)

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    5.074
      
std error ,Se =    √(SSE/(n-2)) =    0.65025

Ho:   ß1=   0          
H1:   ß1╪   0          
n=   14              
alpha =   0.05              
estimated std error of slope =Se(ß1) = Se/√Sxx =    0.65025   /√   5510467   =   0.000
                  
t stat = estimated slope/std error =ß1 /Se(ß1) =    0.0013   /   0.0003   =   4.654
                  
t-critical value=    2.179   [excel function: =T.INV.2T(α,df) ]          
Degree of freedom ,df = n-2=   12              
p-value =    0.0006              
decison :    p-value<α , reject Ho              
Conclusion:   Reject Ho and conclude that cigarette consumption does affect the death rate from bladder cancer at α=0.05

d)

p-value =    0.0006              
decison :    p-value>α=0.01 ,do not reject Ho              
Conclusion: do not Reject Ho and conclude that cigarette consumption does not affect the death rate from bladder cancer at α=0.01