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A statistical test, known as the Student's T-test, may be used to determine if two sample means taken from the same universe are significantly different (38).

In the cases analyzed, average annual miles traveled by bicyclists are studied. One group of the respondents stated that their bicycles were equipped with odometers or other measuring devices. The other group stated that they did not use an odometer, and therefore the mileage figures provided were estimates.

The results of each sample are as follows:

Those with Odometers

                  Average Miles = 2,254 (X1)
             Standard Deviation = 2,027* (S1)
                    Sample Size = 1,120 (N1)

Those without Odometers

                  Average Miles = 2,350 (X2)
             Standard Deviation = 2,116 (S2)
                    Sample Size = 2,105 (N2)

The two mileages reported come from the same universe having the respective means 1 and 2 . The hypotheses are:

H0: 1 = 2, and the difference is merely due to chance.

H1: 1 is not equal to  2 , and there is a significant difference between the groups.

Under the hypothesis H0, both groups come from the same population. The mean and standard deviation of the difference in means are given by


X1-X2 = 0


sigma X1-X2
=\/S12/N1+S22/N2 = 
         \/(2,027)2/1,120+(2,116)2/2,105 = 76.1

where we have used the sample standard deviations as estimates of sigma1 and sigma2. Then, Z(strikethrough), the test statistic, is calculated

Z(strikethrough) =    X1-X2
sigma X1-X2
=2,254-2,350 = -1.26

For a two-tailed test. the results are significant at

a .01 level if Z(strikethrough) lies outside the range -2.58 to +2.58. Hence, we conclude, with 99 percent confidence, that there is no significant difference between the groups with regard to the reported mileages.

*The standard deviation is large due to the number of respondents (almost 10 percent) who reported traveling over 5,000 miles.

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