Applied Statistics and Probability for Engineers

10-4 PAIRED t-TEST 353

This confidence interval is also valid for the case where , because s^2 Destimates D^2 

V(X 1 X 2 ). Also, for large samples (say, n30 pairs), the explicit assumption of normality

is unnecessary because of the central limit theorem.

EXAMPLE 10-10 The journal Human Factors(1962, pp. 375-380) reports a study in which n14 subjects

were asked to parallel park two cars having very different wheel bases and turning radii. The

time in seconds for each subject was recorded and is given in Table 10-3. From the column of

observed differences we calculate and sD12.68. The 90% confidence interval for

D 1  2 is found from Equation 9-24 as follows:

Notice that the confidence interval on Dincludes zero. This implies that, at the 90% level of con-

fidence, the data do not support the claim that the two cars have different mean parking times  1

and  2. That is, the value D 1  2 0 is not inconsistent with the observed data.

EXERCISES FOR SECTION 10-4

4.79 D7.21

1.211.771 1 12.68 2
114 D1.21 1.771 1 12.68 2
114

dt0.05,13 sD
1 n Dd t0.05,13 sD
1 n

d1.21

^21 ^22

Table 10-3 Time in Seconds to Parallel Park Two

Automobiles

Automobile Difference

Subject 1(x 1 j)2(x 2 j)(dj)

1 37.0 17.8 19.2

2 25.8 20.2 5.6

3 16.2 16.8 0.6

4 24.2 41.4 17.2

5 22.0 21.4 0.6

6 33.4 38.4 5.0

7 23.8 16.8 7.0

8 58.2 32.2 26.0

9 33.6 27.8 5.8

10 24.4 23.2 1.2

11 23.4 29.6 6.2

12 21.2 20.6 0.6

13 36.2 32.2 4.0

14 29.8 53.8 24.0

must be normal? Use a normal probability plot to investigate

the normality assumption.

10-35. Consider the parking data in Example 10-10. Use

the paired t-test to investigate the claim that the two types of

cars have different levels of difficulty to parallel park. Use

0.10. Compare your results with the confidence interval

constructed in Example 10-10 and comment on why they are

the same or different.

10-33. Consider the shear strength experiment described in

Example 10-9. Construct a 95% confidence interval on the

difference in mean shear strength for the two methods. Is the

result you obtained consistent with the findings in Example

10-9? Explain why.

10-34. Reconsider the shear strength experiment described

in Example 10-9. Do each of the individual shear strengths

have to be normally distributed for the paired t-test to be ap-

propriate, or is it only the difference in shear strengths that

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