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 not be reject the null hypothesis.

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Given the test statistic of 2.75 and a two-tailed test at a 5% level of significance, we typically compare the test statistic to critical values from the standard normal distribution (Z-distribution) because the population standard deviations are assumed to be known. For a 5% level of significance in a two-tailed test, the critical values are approximately ±1.96. Since 2.75 is greater than 1.96, the null hypothesis should be rejected.

In Testing the Difference Between Two Population Means Using Two