Question

1. What is a p-value and how is it used to make a decision about the null hypothesis?
2. How is the p-value related to the test statistic?
3. Explain whether or not rejecting the null hypothesis makes the alternative hypothesis true and why.
4. If I conduct a hypothesis testing with Type I error set at 0.05 and a resulting p-value of 0.3, what would my conclusion be?

Answer 1

The P value, or calculated probability, is the smallest level of significance. The probability of finding the observed, or more extreme, results when the null hypothesis (H₀) of a study question is true – the definition of ‘extreme’ depends on how the hypothesis is being tested. P is also described in terms of rejecting H₀ when it is actually true, however, it is not a direct probability of this state.

So the p-value makes the decision of the null hypothesis on the basis of the level of significance. So if p-value is higher than Alpha then the null hypothesis is accepted and if it is lower than alpha then the null hypothesis is rejected.

• Pr( X >= x | H ) for right tail event,
• Pr( X <= x | H ) for left tail event,
• 2 Min{Pr( X >= x | H ), Pr( X >= x | H )} for double tail event.

Rejecting the null hypothesis makes the alternative hypothesis true because the alternative hypothesis is exactly the opposite of the null hypothesis.

For example Null Hypothesis: Mean marks of class 1 is equal to the mean marks of class 2

Alternative Hypothesis: Mean marks of class 1 is not equal to the mean marks of class 2

Type 1 error = 0.05 and p-value = 0.3

Since the p-value is greater than type 1 error so the null hypothesis is accepted.