In testing for differences between the means of two independent populations if the test statistic is very large,then the p-value of the test should be very small.

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This is true because a large test statistic means that the difference between the sample means is large, which makes it less likely to have occurred by chance. Therefore, the p-value, which represents the probability of obtaining a test statistic as extreme or more extreme than the observed one under the null hypothesis, should be very small if the difference is statistically significant.

In Testing for Differences Between the Means of Two Independent