Multiple Choice
Which of the following is not true when testing a claim about a standard deviation or variance ()?
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9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
Multiple Choice
Which of the following scenarios would result in a null hypothesis and an alternative hypothesis ?
A
A researcher wants to test if the proportion of defective products is exactly .
B
A researcher wants to test if the proportion of defective products is less than .
C
A researcher wants to test if the proportion of defective products is not equal to .
D
A researcher wants to test if the proportion of defective products is greater than .
Verified step by step guidance1
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.
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.
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%.
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%.
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 \(p < 0.44\).
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