Question

In: Statistics and Probability

A researcher suspects that the actual prevalence of generalized anxiety among children and adolescents is higher...

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%. What should the researcher's conclusion be for a 5% significance level?

A.

We fail to reject H0 at the 5% because 1.09 is less than 1.96. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.
B.

We fail to reject H0 at the 5% because .092 is less than 1.645. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.
C.

We reject H0 at the 5% level because -57.53 is less than -1.96. We do have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.
D.

We fail to reject H0 at the 5% because -1.12 is greater than -1.645. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.

Solutions

Expert Solution

Population proportion = 3.9% or 0.039

Sample size = 98

Sample proportion = 6.1% or 0.061

Part D is right but the negative signs are wrong since its a right-tailed test. As clearly its mentioned that 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.

orchestra answered 2 years ago
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