SOLUTION: A researcher suspects that the actual prevalence of generalized anxiety among children and adolescents is higher than the previously reported prevalence of generalized anxiety diso
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Question 1127356: A researcher suspects that the actual prevalence of generalized anxiety among children and adolescents is higher than the previously reported prevalence of generalized anxiety disorder among children and adolescents. The previously reported prevalence of generalized anxiety disorder among children and adolescents is 3.9%, and the researcher conducts a study to test the accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98 children and adolescents from various pediatricians' offices and tests them for generalized anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized anxiety disorder among the participants of the study is 6.1%. The researcher's hypothesis, for a level of significance of 5%, should resemble which of the following sets of hypothesis?
A. H0: p > .039; H1: p = .039; alpha= .05
B. H0: p = .039; H2: p > .039; alpha= .05
C. H0: p = .039; H2: p > .039; alpha= .95
D. H0: p > .039; H1: p = .039; alpha= .95
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Rule: The null hypothesis will always have an equal sign in it somehow. So the sign will be a straight up "equal sign" or it will be a "greater than or equal to" sign, or a "less than or equal to sign". The key here is that "equal" is found in each symbol.
Why is this rule the case? Because we want the parameter (in this case p) to be a certain fixed value, and only one fixed value, which we will form a distribution based on that parameter. This distribution is the null distribution in which we test the hypothesis. If we had a null of something like p > 0.039 then we would have to test all the values of p that are larger than 0.039, which are infinitely many. Therefore, saying p = 0.039 is much more clear to help build a distribution.
Based on that rule, this means the answer is between B and C. We can further eliminate choice C because alpha is not 0.95; but instead, alpha is actually 0.05 as this is the significance level 5%. The two hypothesis are: either p = 0.039 (null hypothesis) or p > 0.039 (alternative hypothesis)
Final Answer: B. H0: p = .039; H2: p > .039; alpha= .05
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Side Note: The text states that "A researcher suspects that the actual prevalence of generalized anxiety among children and adolescents is higher than the previously reported prevalence of generalized anxiety disorder among children and adolescents". The keyword "higher" is underlined which helps us determine that p > 0.039 is one hypothesis
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