9.2
Null and Alternative Hypotheses
The actual hypothesis testing begins by considering two hypotheses. They are termed the null hypothesis and the alternative hypothesis. These hypothes…
Hypothesis testing begins with stating at least two contrasting statements of a claim about a population characteristic.
Consider an example of studying the proportion of healthy and scabbed apples from a cultivar.
To test this, we may begin by stating that 'the cultivar produces an equal number of healthy and scabbed apples.' This statement is the null hypothesis, denoted as H0, and is represented as follows.
Alternatively, the statement that 'the cultivar produces a different proportion of the healthy and scabbed apples' has an opposite viewpoint than the previous one. This statement is the alternative hypothesis, denoted as H1, and is represented as follows.
An alternative hypothesis should not state that the parameter value equals an exact number or a predetermined fixed value.
For instance, 'proportion of scabbed apples harvested from the cultivar is 0.2' is not an appropriate alternative hypothesis as one may get that exact value of proportion just by chance alone but may not get enough data to support the claim of proportion being precisely 0.2.
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Q1: What is the null hypothesis in hypothesis testing?
The null hypothesis, denoted H0, is a statement claiming no difference or relationship between variables—essentially the status quo. In the apple cultivar example, H0 states the cultivar produces an equal number of healthy and scabbed apples. It represents the default assumption that must be tested against sample data.
Q2: How does the alternative hypothesis differ from the null hypothesis?
The alternative hypothesis, denoted H1 or Ha, contradicts the null hypothesis and represents what researchers aim to prove. While H0 claims no difference, H1 asserts a different relationship exists. For the apple example, H1 states the cultivar produces a different proportion of healthy and scabbed apples than H0 claims.
Q3: Why can't an alternative hypothesis state an exact parameter value?
An alternative hypothesis cannot specify an exact value because that precise value might occur by chance alone without supporting the researcher's claim. For instance, stating the proportion of scabbed apples is exactly 0.2 is inappropriate; you might obtain that value randomly without sufficient evidence to confirm it as the true population parameter.
Q4: What does it mean to reject or fail to reject the null hypothesis?
Rejecting H0 means sample data sufficiently supports the alternative hypothesis, prompting action or conclusion change. Failing to reject H0 means sample data lacks sufficient evidence against it, so the status quo remains. These are the only two decision options after examining sample evidence in hypothesis testing.
Q5: How does sample data guide decisions in hypothesis testing?
Sample data provides evidence to determine which hypothesis the population likely supports. Researchers examine this evidence to decide whether to reject H0 or decline to reject it. The strength and direction of sample results determine whether sufficient evidence exists to conclude the alternative hypothesis is true.
Q6: What role do null and alternative hypotheses play in statistical inference?
Null and alternative hypotheses form the foundation of hypothesis testing by establishing two contradictory claims about a population. They structure the investigation by defining what will be tested and what conclusion follows if evidence supports each hypothesis. This framework enables researchers to make objective decisions based on sample data.
Q7: What happens after you decide to reject or fail to reject the null hypothesis?
After the decision, further analysis follows through methods like testing a claim about population proportion or evaluating critical values and significance level. The decision determines which hypothesis is supported and guides subsequent statistical procedures. Understanding errors in hypothesis tests also becomes important for interpreting the reliability of your conclusion.