Question

The sample data below are the index of exposure (x) to radioactive waste for nine different Oregon counties and cancer mortality rate (y) (deaths per 100,000). X 2.492.57 3.41 1.25 1.62 3.83 11.64 6.41 8.34 y 147.1|130.1 129.9 113.5 1375 162.3207.5 177.9210.3 a) Find the linear correlation coefficient r. (2 points) b) Do the data provide sufficient evidence to conclude that index of exposure and cancer mortality rate are linearly correlated? (3 points) c) Find the linear regression equation and find the mortality rate for a county in Oregon with an index exposure of 5.6. (4 points)

Answer 1

Solve using Excel functions:

a) Correlation coefficient: r = CORREL(x,y) = 0.926

b) n = 9, Degrees of freedom: df = n-2 = 7, Level of significance: α = 0.05

H₀: ρ = 0, There is not sufficient evidence that index of exposure and cancer mortality rate are linearly correlated

H₁: ρ ≠ 0, There is sufficient evidence that index of exposure and cancer mortality rate are linearly correlated

Test statistic: t = r*((1-r*r)/(n-2))^0.5 = 0.926*((1-0.926*0.926)/(9-2))^0.5 = 0.132

Critical value (Using Excel function T.INV.2T(probability,df)) = T.INV.2T(0.05,7) = 2.365

Since test statistic is less than critical value, we fail to reject H₀.

So, there is not sufficient evidence that index of exposure and cancer mortality rate are linearly correlated.

c) y = a+bx

a = INTERCEPT(y,x) = 114.72

b = SLOPE(y,x) = 9.23

y = 114.72 + 9.23x

Index exposure:x = 5.6

Mortality rate: y = 114.72 + 9.23*5.6 = 114.72+51.69 = 166.41