Ken and Billy both live in the same neighborhood, and work at the university. Ken drives to work, Billy rides his bicycle. You - a budding statistician - have been asked to settle an argument. Ken believes that more often than not, his commuting time via his drive is less than Billy's. Billy believes that this is not so, due to traffic volume and traffic lights. Over the period of one month, the statistician randomly selects eight days for Ken and eight days for Billy. On each day, they will be asked to measure, to the nearest tenth of a minute, the amount of time it takes them to get from their home to the university campus.

The commuting times are given on each randomly chosen day, for each person.

Ken: 24, 13.6, 9.7, 21.6, 13.8, 10.6, 9.6, 14.9;

Billy: 20.4, 20.3, 20.1, 17.1, 16.8, 19.8, 19.9, 17.1;

Carry out a statistical test, the results of which will be used to settle Ken and Billy's argument.

(a) Using the technology available to you, visually and statistically inspect this data. From this, construct the most appropriate statistical hypotheses.

A.H0:D=0HA:D<0H0:D=0HA:D<0

B.H0:D=0HA:D>0H0:D=0HA:D>0

C.H0:D=0HA:D0H0:D=0HA:D0

D.H0:Ken=BillyHA:Ken<BillyH0:Ken=BillyHA:Ken

E.H0:Ken=BillyHA:Ken>BillyH0:Ken=BillyHA:Ken>Billy

F.H0:~Ken=~BillyHA:~Ken~BillyH0:~Ken=~BillyHA:~Ken~Billy

G.H0:~Ken=~BillyHA:~Ken>~BillyH0:~Ken=~BillyHA:~Ken>~Billy

H.H0:~Ken=~BillyHA:~Ken<~BillyH0:~Ken=~BillyHA:~Ken<~Billy

I.H0:Ken=BillyHA:KenBillyH0:Ken=BillyHA:KenBilly

(b) Find the value of the test statistic for this test, use at least one decimal in your answer.

Test Statistic = equation editorEquation Editor

(c) Determine thePP-value of your statistical test in part (c), and report it to at least three decimal places.

P=

(d) At=0.05=0.05, this data indicates that you will

reject/not reject

the null hypothesis. You can tell Ken that his commute time is

same as/faster than/slower than

Billy's.