A journal reported a study in which n = 10 subjects were asked to parallel park

Question

A journal reported a study in which n = 10 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 the table below.

a. Find a 90% CI on the mean difference in times.

b. 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.

Automobile Subject    1(X1j) 2(X2j) 1 37.0 17.8 2 25.8 20.2 3 16.2 16.8 4 24.2 41.4 5 22.0 21.4 6 33.4 38.4 7 23.8 16.8 8 58.2 32.2 9 33.6 27.8 10 24.4 23.2

Explanation / Answer

so Average Differeence between X1 - X 2 = 4.26

Std. Deviation of the difference s= 12.02

SE( ¯d) = s/ n = 12.02/ 10 = 3.801

tcritical for alpha = 0.10 and dF = 10 -1 = 9

tcritical (0.05,9) = 1.833

90% CI on the mean difference in times = (X1 - X 2) +- tcritical (0.05,9) * SE( ¯d)

= 4.26 +- 1.833 * 3.801

= ( - 2.707, 11.227)

b. Test Statistic

t = (X1-bar - X2 -bar )/ SE = (29.86 - 25.6)/ 3.801 = 1.12

Here, t < tcritical (0.05,9) , so we cannot the reject the null hypothesis and can say there is no difference in means of both paired data.and claim that the two types of cars have no different level of difficulty to parellel park.

Automobile Subject    1(X1j) 2(X2j) X1 - X2 1 37 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 21.4 0.6 6 33.4 38.4 -5 7 23.8 16.8 7 8 58.2 32.2 26 9 33.6 27.8 5.8 10 24.4 23.2 1.2 42.6 Sum 4.26 Average 12.01926 Std. Dev.

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