QUESTION 8 ( 2 0 marks)   In the past 20 years, society in general and the judicial system in particular have altered their opinions on the seriousness of drunken driving

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QUESTION

8

(

2

0

marks)

 

In the past 20 years, society in general and the judicial system in particular have altered

their opinions on the seriousness of drunken driving. In most jurisdictions of the United

States, driving an automobile with blood alcohol content (BAC) level in

ex

cess of 0.08

is a felony. [

0.08 BAC is legally impaired and it is illegal to drive at this level]

. Because

of a number of factors, it is difficult to

provide guidelines on when it is safe for someone

who has consumed alcohol to drive a car. In an experime

nt to examine the relationship

between blood alcohol level and the weight of a drinker, 50 men of varying weights were

each given three (3) beers to drink, and I hour later their blood alcohol content level was

measured. The data reading of the two variab

les are as follows:

 

Weight

(in lbs)

Blood Alcohol Level

Weight (in lbs)

Blood Alcohol Level

214

0.07

176

0.07

270

0.09

169

0.06

185

0.07

170

0.07

196

0.07

197

0.09

175

0.10

213

0.07

153

0.09

210

0.08

165

0.06

220

0.07

215

0.12

215

0.06

216

0.09

173

0.09

190

0.09

196

0.06

204

0.10

216

0.09

153

0.06

161

0.06

209

0.06

208

0.08

206

0.10

176

0.08

190

0.09

179

0.07

220

0.08

193

0.08

266

0.11

224

0.08

224

0.09

233

0.11

229

0.11

152

0.07

211

0.07

172

0.07

200

0.07

155

0.05

201

0.08

169

0.08

212

0.09

149

0.09

223

0.08

207

0.06

148

0.08

217

0.08

 

The following is the EXCEL printout of the regression analysis of the two variables

.

 

Regression Statistics

Multiple R

0.41773

R Square

0.17449

Adjusted

R Square

0.15730

Standard Error

0.01398

Observations

50

 

________________________________________________

________________________

STA 1600

Probability and Statistics

Page

6

of

6

ANOVA

df

SS

MS

F

Significance

F

Regression

1

0.00198

0.00198

10.146

0.00254

Residual

48

0.00937

0.00019

Total

49

0.01132

 

Coefficients

Standard

Error

t Stat

P

-

value

Lower

95%

Upper

95%

Intercept

0.03318

0.01402

2.3661

0.02206

0.00498

0.06137

Weight (in lbs)

0.00022

0.00007

3.1853

0.00254

0.00008

0.00036

 

Required:

Using the EXCEL output (assuming that the two variables are normally distributed) to

answer the following questions:

a)

Provide the linear

regression model equation that relates blood alcohol content

(BAC) and body weight (lbs)

.

(2

marks)

b)

Explain the strength of the

correlation

(expressed in percentage)

between blood

alcohol content and body weight?

(2 marks)

c)

Interpret the meaning of the slope of the linear model regression equation.

(2 marks)

d)

Interpret the meaning of R Square (the coefficient of determination) of this linear

model regression equation.

(2 marks)

e)

Estimat

e the blood alcohol content (BAC) level of a 250 pounds drinker after 1

-

hour of consuming 3 glasses of beer?

Based on your calculated value, is the 250

pounds drinker legally impaired? Explain.

(3

marks)

f)

Based on your estimation in part (

e

), construct a 95% confidence interval for the

average blood alcohol content (BAC) of the drinker after 1 hour of consuming 3

glasses of beer. Provide a statement for your answer.

(

5

marks)

g)

At the 0.05 level of significance, is there sufficient

evidence to indicate a linear

relationship between

blood alcohol content (BAC) level and weight of drinker?

1)

Provide the hypothesis statement

.

(2 marks)

2)

Based on p

-

value, is there evidence to indicate a linear

relationship

b

etween the two v

ariables? Provide a statement for your statistical

conclusion.