A friend has performed a significance test of the null hypothesis that two means

Question

A friend has performed a significance test of the null hypothesis that two means are equal. His report states that the null hypothesis is rejected in favor of the alternative that the first mean is larger than the second. In a presentation on his work, he notes that the first sample mean was larger than the second mean and this is why he chose this particular one-sided alternative. Explain what is wrong with your friend's procedure and why. The null hypothesis in this case should have been that the two means were not equal. We should never choose a one-sided alternative. The first mean can never be larger than the second mean; this indicates a mistake was made during statistical analysis. We should only choose a one-sided alternative if we have some reason to expect a specific directional outcome before looking at the sample results. The null hypothesis in this case should have been that the first mean is larger than the second. Suppose he reported t = 1.75 with a rho-value of 0.06. What s the correct rho-value that he should report?

Explanation / Answer

Since he chose to do one tailed test whereas in this case, two tailed test should have been performed. The actual p - value would be double than his reported p - value.

Reported p - value= 0.06

So,

Correct p - value = 2(0.06) = 0.12

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