In testing the difference between two population means using two independent samples, the population standard deviations are assumed to be known, and the calculated test statistic equals 2.75. If the test is two-tail and 5% level of significance has been specified, the conclusion should be not to reject the null hypothesis.

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At a 5% significance level for a two-tailed test, the critical values for a z-test (assuming the population standard deviations are known, thus a z-test applies) are approximately ±1.96. A test statistic of 2.75 exceeds this critical value, indicating that the null hypothesis should be rejected.

In Testing the Difference Between Two Population Means Using Two