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A sports writer wished to see if a football filled with helium travels farther,...

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A sports writer wished to see if a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 18 adult male volunteers. These volunteers were randomly divided into two groups of nine subjects each. Group 1 kicked a football filled with helium to the recommended pressure. Group 2 kicked a football filled with air to the recommended pressure. The mean distance for group 1 was 30 metres, with a standard deviation s_1s_1 = 8 metres. The mean distance for group 2 was 26 metres, with a standard deviation s_2s_2 = 6 metres. Assume the two groups of kicks are independent. Let \mu_1\mu_1 and \mu_2\mu_2 represent the mean distance we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium- and an air-filled football. Assume that two-sample t-procedures are safe to use.

Suppose the researcher had wished to test the hypotheses

H0: \mu_1 = \mu_2\mu_1 = \mu_2,  Ha: \mu_1 > \mu_2\mu_1 > \mu_2.

The numerical value of the two-sample t statistic (in 2 decimal places) is equal to .

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