Knowing When to Use a Hypothesis Test
Hypothesis testing is a scientific procedure for asking and answering questions. Hypothesis tests help people decide whether existing claims about a population are true, and they’re also commonly used by researchers to see whether their ideas have enough evidence to be declared statistically significant.
Solve the following problems about using a hypothesis test.
Which of the following statements as currently written could be tested using a hypothesis test?
A. An automobile factory claims 99% of its parts meet stated specifications.
B. An automobile factory claims that it produces the best-quality cars in the country.
C. An automobile factory claims that it can assemble 500 automobiles an hour when the assembly line is fully staffed.
D. Choices (A) and (B)
E. Choices (A) and (C)
Answer: E. Choices (A) and (C) (An automobile factory claims 99% of its parts meet stated specifications; an automobile factory claims that it can assemble 500 automobiles an hour when the assembly line is fully staffed.)
A hypothesis test is a statistical procedure undertaken to test a quantifiable claim. “The best-quality cars” isn’t quantifiable on its own and can’t be tested in this manner, while the other two claims can.
If the “best quality” is defined, for example, as having “an average of 30 amenities per vehicle,” then a hypothesis test could be devised.
Which of the following scenarios as currently stated could not involve a hypothesis test without further clarification?
A. A political party conducts a survey in an attempt to contradict published claims of the proportion of voter support for a proposed law.
B. A commercial laboratory does sample tests on a hand sanitizer to see whether it kills the percentage of bacteria claimed by the manufacturer.
C. A school gives its students standardized tests to measure levels of achievement compared to prior years.
D. A laboratory takes samples of a yogurt to see whether the manufacturer has met its published claim of being 99% fat free.
E. A university evaluation group gives random surveys to students to see whether university claims regarding the proportion of students who are satisfied with student life are valid.
Answer: C. A school gives its students standardized tests to measure levels of achievement compared to prior years.
A hypothesis test is a statistical procedure undertaken to test a quantifiable claim. No quantifiable claim is clearly defined in the preceding statement, and therefore no hypothesis test is possible without further clarification.
If you’re told that last year’s standardized test yielded an average math subscore of 80, you could test whether this year’s students perform significantly better. But as currently stated, you’re not given a clear definition of the population value (parameter) of interest.
If you need more practice on this and other topics from your statistics course, visit 1,001 Statistics Practice Problems For Dummies to purchase online access to 1,001 statistics practice problems! We can help you track your performance, see where you need to study, and create customized problem sets to master your stats skills.