Question

A food processor claims that at most 10% of her jars of instant coffee contain less coffee than claimed on the label. To test this claim, 16 jars of her instant coffee are randomly selected.

(a) Formulate the null and alternative hypotheses for testing the food processor's claim.

Answer 1

The null hypothesis (H0) for testing the food processor's claim is that at most 10% of the jars contain less coffee (H0: p ≤ 0.10), and the alternative hypothesis (Ha) is that more than 10% do (Ha: p > 0.10).

Step-by-step explanation:

To test the food processor's claim, we need to formulate the null and alternative hypotheses. The null hypothesis (H0) represents the status quo or the claim that needs to be tested, while the alternative hypothesis (Ha) represents what we are trying to find evidence for.

In this case, the null hypothesis would be that at most 10% of the jars contain less coffee than claimed on the label. This can be stated as H0: p ≤ 0.10, where p represents the true proportion of jars with less coffee than stated. The alternative hypothesis is that more than 10% of the jars contain less coffee than claimed, which can be stated as Ha: p > 0.10.

The choice of the alternative hypothesis is based on the claim we are testing against. If the processor's claim is that at most 10%, this indicates we are looking for evidence that suggests the proportion is greater than 10%.