You may assume normal distributions in each case. A dealer of a certain Japanese

Question

You may assume normal distributions in each case.

A dealer of a certain Japanese car claims that it is easier to change spark plugs on a four -cylinder model that he sells than on a comparable U.S. model. To test the claim, eight mechanics of proven ability who were not employees of the dealership nor of the U.S. model being tested each were assigned to change spark plugs on the two models. Their times (in minutes) are recorded as follows. At the 1% level of significance, is the dealer's claim valid?

Explanation / Answer

Solution:

Here, we have to use the paired t test for checking the significant difference between the two population means.

H0: µ1 = µ2 versus Ha: µ1 < µ2

= 0.01

Test statistic formula is given as below:

Test statistic = t = Dbar / [Sd/sqrt(n)]

Calculation table is given as below:

Japanese Model

U.S. Model

Di

(Di - DBar)^2

15

19

-4

9.765625

21

24

-3

4.515625

22

19

3

15.015625

13

16

-3

4.515625

18

16

2

8.265625

21

23

-2

1.265625

20

19

1

3.515625

25

26

-1

0.015625

Dbar =

-0.875

We are given

Sample size = n = 8

Degrees of freedom = 8 – 1 = 7

Sd = 2.5877

Test statistic = t = -0..875/[2.5877/sqrt(8)]

Test statistic = t = -0.9564

Critical value = -2.9980

P-value = 0.1854

P-value is greater than alpha value.

So, we do not reject the null hypothesis that there is no any significant difference in the average time for Japanese model and U.S. model.

Japanese Model

U.S. Model

Di

(Di - DBar)^2

15

19

-4

9.765625

21

24

-3

4.515625

22

19

3

15.015625

13

16

-3

4.515625

18

16

2

8.265625

21

23

-2

1.265625

20

19

1

3.515625

25

26

-1

0.015625

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