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. (a) 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 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. The first mean can never be larger than the second mean; this indicates a mistake was made during statistical analysis. We should never choose a one-sided alternative. (b) Suppose he reported t = 1.75 with a P-value of 0.06. What is the correct P-value that he should report?

Explanation / Answer

sOL:

Null hypotehsis:

Means are equal;

H0: mean1=mean2

Alternative Hypothesis:

H1: mean1>mean2

Here it is directional one sided

> means increase

Right tail t test

Answer B .

we should choose one sided alternative

Solutionb:

if p<0.05 only then we can reject null hypothesis and favours alternative hypothesis.

Here p>0.05 0.06 Correct p value is

P<0.05

here ccorrect p=0.05

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