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 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.

(a) Explain what is wrong with your friend's procedure and why.

We should never choose a one-sided alternative.

The null hypothesis in this case should have been that the two means were not equal.

We should only choose a one-sided alternative if we have some reason to expect a specific directional outcome before looking at tech sample results.

The null hypothesis in this case should have been that the first mean is larger than the second.

The first mean can never be larger than the second mean; this indicates a mistake was made during statical analysis.

(b) Suppose he reported t = 1.80 with a P-value of 0.05. What is the correct P-value that he should report?

Answer 1

Solution:-

a) We should only choose a one-sided alternative if we have some reason to expect a specific directional outcome before looking at tech sample results.

b) The correct P-value he should report is 0.10, he should take this hypothesis test as two tailed instead of one tailed test.