Question

7. In a 1973 Technometrics article, the authors examined mortality rates (deaths per 100,000 population) for 60 metropolitan areas. The following is MINITAB output for a fit of the least-squares line to predict mortality from ambient SO₂ measured as a "pollution potential."

The regression equation is

TOTAL MORT RATE = 918 + 0.418 SO2 POTENTIAL

Predictor                        Coef               SE Coef               T              P

Constant                        917.887            9.644               95.18        0.000

SO2 POTENTIAL        0.4179               0.1166              3.58         0.001

S = 56.7657              R-Sq =                             R-Sq(adj) =

Analysis of Variance

Source	DF	SS	MS	F	P
Regression	1	41411	41411	12.85	0.001
Residual Error	58	186896	3222
Total	59	228308

6. Test the null hypothesis that the regression coefficient for SO₂ is no greater than 0.4 vs. the alternative that it is greater than 0.4. Use α = 0.05.

????

Answer 1

we have given minitab output of the simple linear regression :

y as mortality and x is SO2 potential

## a) Test the null hypothesis that the regression coefficient for SO2 is no greater than 0.4 vs. the alternative that it is greater than 0.4. Use α = 0.05.

## to test : Ho = β1 = 0.4 vs H1 ; β 1 > 0.4

where β1 is coefficient for SO2 potential .

## test statistics : t = (b1 - β1 ) / se(b1)

here b1 =  0.4179 and se(b1) = 0.1166

t = (0.4179 - 0.4) / 0.1166

t = 0.1535

## p value = 0.4394 ( use t statistical table)

## Decision : we reject Ho if p value is less than α value using p value approach here

p value is greater than α value , we fail to reject Ho .

## Conclusion : there is not enough evidecen to conclude that the coefficient of SO2 potential is

greater than 0.4

ie it is equal to the 0.4