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Some people believe that higher-octane fuels result in better gas mileage for th

ID: 3264511 • Letter: S

Question

Some people believe that higher-octane fuels result in better gas mileage for their car. To test this claim, a researcher randomly selected

1111

individuals (and their cars) to participate in the study. Each participant received 10 gallons of gas and drove his car on a closed course. The number of miles driven until the car ran out of gas was recorded. A coin flip was used to determine whether the car was filled up with 87-octane or92-octane first, and the driver did not know which fuel was in the tank.

87-octane

234234

257257

244244

216216

113113

288288

316316

229229

193193

205205

546546

92-octane

238238

239239

230230

224224

118118

297297

351351

241241

185185

209209

562562

(a) Why is it important that the matching be done by driver and car?

A.

So that all the trials can be done at the same time

B.

How someone drives and the car they drive result in different fuel consumption

C.

Cuts the cost of doing the research

D.

So that each driver can determine which fuel is best for their car

(b) Why is it important to conduct the study on a closed track?

A.

So that all drivers and cars have similar driving conditions

B.

So that the researcher can watch the drivers

C.

So that each car travels the same distance

(c) The normal probability plots for miles on87-octane and miles on 92-octane are shown.

-2007000         10087 OctanePercent

-2007000         10092 OctanePercent

Are either of these variables normally distributed?

A.

No, neither variable is normally distributed.

B.

Yes, 92-octane is normally distributed.

C.

Yes, both variables are normally distributed.

D.

Yes, 87-octane is normally distributed.

(d) The differences are computed as 92-octane minus 87-octane. The normal probability plot of the differences is shown. Is there reason to believe that the differences are normally distributed?

Yes

No

(e) The researchers used a statistical software package to determine whether the mileage from 92-octane is greater than the mileage from 87-octane. The results are given below.

Paired T-Test and CI: 92 Octane, 87 Octane

Paired T for 92 Octane87Octane

N

Mean

StDev

SE Mean

92 Octane

11

258.273

108.924

32.842

87 Octane

11

263.091

115.161115.161

34.722

Difference

11

4.818

14.682

4.427

T-Test of mean difference

equals=0

(vs

greater than>0):

T-Valueequals=1.09

P-Value=0.151

What do you conclude at

=0.05?

Why?

A.

Reject the null hypothesis because the P-value is greater than

0.05.

B.

Fail to reject the null hypothesis because the P-value is greater than

0.050.05.

C.

Reject the null hypothesis because the P-value is less than

0.05.

D.

Fail to reject the null hypothesis because the P-value is less than

0.05.

87-octane

234234

257257

244244

216216

113113

288288

316316

229229

193193

205205

546546

92-octane

238238

239239

230230

224224

118118

297297

351351

241241

185185

209209

562562

Explanation / Answer

Part a )

How someone drives and the car they drive result in different fuel consumption

Part b )

So that all drivers and cars have similar driving conditions

Part C )

Histogram for 87 octance

Histogram for 92 octance

No, neither variable is normally distributed.

Part d ) Yes,

Part e ) Here , P-value > 0.05 so we fail to reject H0

Fail to reject the null hypothesis because the P-value is greater than 0.05.

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