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 10 cars, chosen at random. 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 the table below. 78 Car Brand 1 Brand 2 Difference (Brand 1- Brand 2) Send data to calculator 1 2 0.51 0.56 0.62 0.58 0.58 6 10 0.42 0.48 0.61 0.34 0.62 0.57 0.29 0.57 0.47 0.31 0.21 0.55 0.44 0.46 0.62 -0.06 0.27 0.05 0.11 0.27 0.21 -0.07 0.17 -0.12 0.00 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 μ (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 complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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Transcribed Image Text: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 10 cars, chosen at random. 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 the table below. 6 7 8 9 Car Brand 1 Brand 2 Difference (Brand 1- Brand 2) Send data to calculator 1 0.51 2 0.56 0.57 0.29 3 4 5 10 0.62 0.58 0.58 0.42 0.48 0.61 0.34 0.62 0.57 0.47 0.31 0.21 0.55 0.44 0.46 0.62 -0.06 0.27 0.05 0.11 0.27 0.21 0.07 0.17 -0.12 0.00 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 μ (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 complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.)

(a) State the null hypothesis H and the alternative hypothesis H₁.
Ho
:
H₁ :
(b) Determine the type of test statistic to use.
Type of test statistic: Chi-Square ▼
(c) Find the value of the test statistic. (Round to three or more decimal places.)
0
(d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.)
and 0
(e) At the 0.05 level, can the consumer group conclude that the mean tread wears of the brands differ?
Yes No
Degrees of freedom: 0
3.
μ
|x
X
0#0
O
X
S
Р
0=0 OSO 020
0<0
<o
010
0>0

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