Question

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%.
A) For a level of significance of 5%, what should the researcher’s decision rule look like?

Answer 1

Answer:

Since 6.1% is greater than 5%, the results is statistically insignificant

Step-by-step explanation:

If his observation was to be less than 5% it would have been scientifically significant having confidence level of more than 95%, but 6.1% implies the confidence level is less than 95% and statistically insignificant

Answer 2

Answer:

There is insufficient evidence

Step-by-step explanation:

Given : n = 98 p = 0.061 p_0=0.039\alpha=0.05

HYpothesis : H_0:P=0.039 Vs H_1:P>0.039

The test statistic under H o is given by ,

Z=\frac{p-p_0}{\sqrt{p_0q_0/n}}\to N(0,1)

=\frac{0.061-0.039}{\sqrt{0.039*0.961/98}}=1.1250

Critical value : Z_{table }=Z_{\alpha}=Z_{0.05}=1.64

Decision Rule : Here , Z_{stat}=1.1250<Z_{table }=1.64

Therefore , fail to reject H o

Conclusion : Hence , there is insufficient evidence to conclude that the 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