Question

A company want to know whether the use of radial tires instead of regular belted tires improves fuel economy. Twelve cars were equipped with radial tires and driven over a prescribed test course. Without changing drivers, the same cars were then equipped with regular belted tires and driven once again over the test course. The gasoline consumption, in kilometers per liter, was recorded as follows:(using R, I need R code)

Kilometers per Liter

Car Radial Tires

1 4.2

2 4.7

3 6.6

4 7

5 6.7

6 4.5

7 5.7

8 6

9 7.4

10 4.9

11 6.2

12 5.2

Belted Tires

4.1 4.9 6.2 6.9 6.8 4.3 5.7 5.8 6.9 4.7 6 4.9

(1) Do the data provide sufficient evidence to indicate that the mean gasoline consumption for the cars equipped with radial tires is significantly greater than 6.0? Test by using α= .05.

(2) Can we conclude that cars equipped with radial tires give better fuel economy than those equipped with belted tires? Test by using α= .05.

Answer 1

The R code is pasted below.

# ENTERING THE DATA
radial = c(4.2,4.7,6.6,7.0,6.7,4.5,5.7,6.0,7.4,4.9,6.2,5.2)
belted = c(4.1,4.9,6.2,6.9,6.8,4.3,5.7,5.8,6.9,4.7,6.0,4.9)

# IN QUESTION 1, WE HAVE TO PERFORM A RIGHT TAILED, 1 SAMPLE T-TEST
t.test(radial,alternative="greater",mu = 6)
# SINCE P-VALUE > ALPHA = 0.05, WE FAIL TO REJECT H0 AND CONCLUDE THAT THERE IS NOT ENOUGH EVIDENCE TO SUGGEST THAT 'MU' > 6.

# IN QUESTION 2, WE HAVE TO PERFORM A PAIRED SAMPLES T-TEST
t.test(radial,belted,alternative="greater",paired=T)
# SINCE P-VALUE < ALPHA = 0.05, WE REJECT HO AND CONCLUDE THAT RADIAL TIRES GIVE BETTER FUEL ECONOMY.