Question

A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of

10

cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for

20,000

miles, the amount of tread wear (in inches) is recorded, as shown in Table 1.

Car Brand 1 Brand 2 Difference (Brand 1 - Brand 2) 1 0.360 0.279 0.081 2 0.273 0.139 0.134 3 0.329 0.163 0.166 4 0.326 0.222 0.104 5 0.314 0.331 -0.017 6 0.241 0.234 0.007 7 0.262 0.162 0.100 8 0.264 0.280 -0.016 9 0.237 0.119 0.118 10 0.337 0.290 0.047

Table 1

Based on these data, can the consumer group conclude, at the

0.05

level of significance, that the mean tread wears of the brands differ? Answer this question by performing a hypothesis test regarding

μd

(which is

μ

with a letter "d" subscript), the population mean difference in tread wear for the two brands of tires. Assume that this population of differences (Brand 1 minus Brand 2) is normally distributed.

Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic: (Round to at least three decimal places.) The two critical values at the 0.05 level of significance: (Round to at least three decimal places.) and At the 0.05 level, can the consumer group conclude that the mean tread wears of the brands differ? Yes No

Answer 1

Car	Brand1	Brand2	d	d^2
1	0.36	0.279	0.081	0.006561
2	0.273	0.139	0.134	0.017956
3	0.329	0.163	0.166	0.027556
4	0.326	0.222	0.104	0.010816
5	0.314	0.331	-0.017	0.000289
6	0.241	0.234	0.007	4.9E-05
7	0.262	0.162	0.1	0.01
8	0.264	0.28	-0.016	0.000256
9	0.237	0.119	0.118	0.013924
10	0.337	0.29	0.047	0.002209
Total			0.724	0.089616
Number of pairs (n) =		10
d-bar =	0.724/10=0.0724
Sd =	0.064290

The null hypothesis:	H0:
The alternative hypothesis:	H1:

The type of test statistic:

(Choose one) t

The value of the test statistic:
(Round to at least three decimal places.)

t=dbar-0/sd/sqrt(n)

=0.0724/(0.064290/sqrt(10))

=3.561109

t=3.561

value of the test statistic: t=3.561

the 2 critical values are

=T.INV.2T(0.05,9)

=2.262157163

so 2 critical values are

-2.262 and +2.262

The two critical values at the 0.05

level of significance:

-2.262 and +2.262

since t stat>tcrit

Reject Ho and conclude that brand1 and brand 2 means are different.

At the 0.05 level, can the consumer group conclude that the mean tread wears of the brands differ?

YES

ANSWERS IN BOLD