Which of the following scenarios would result in a null hypothesis $p=0.44$ and an alternative hypothesis $p<0.44$?

• A. A researcher wants to test if the proportion of defective products is exactly $44\%$.
• B. A researcher wants to test if the proportion of defective products is less than $44\%$.
• C. A researcher wants to test if the proportion of defective products is not equal to $44\%$.
• D. A researcher wants to test if the proportion of defective products is greater than $44\%$.

Answer: (B)

Verified step by step guidance

1. Understand the meaning of the null hypothesis (\(H_0\)) and alternative hypothesis (\(H_a\)) in hypothesis testing. The null hypothesis usually represents the status quo or a statement of equality, while the alternative hypothesis represents what you want to test or prove.
2. Identify the null hypothesis given: \(H_0: p = 0.44\). This means the researcher assumes the proportion of defective products is 44% unless there is evidence to suggest otherwise.
3. Look at the alternative hypothesis given: \(H_a: p < 0.44\). This indicates the researcher is testing if the proportion of defective products is less than 44%.
4. Match the alternative hypothesis to the scenario. Since \(H_a\) is testing for a proportion less than 44%, the scenario must be one where the researcher wants to check if the defective rate is lower than 44%.
5. Conclude that the correct scenario is: 'A researcher wants to test if the proportion of defective products is less than 44%,' because this matches the alternative hypothesis \(p < 0.44\).