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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 4.1%, 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 6.8%. The researcher’s hypothesis, for a level of significance of 5%, should resemble which of the following sets of hypothesis?

A) H₀: p > .041; H₁: p = .041; alpha= .05

B) H₀: p > .041; H₁: p = .041; alpha= .95

C) H₀: p = .041; H₁: p > .041; alpha= .05

D) H₀: p = .041; H₁: p > .041; alpha= .95

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 4.1%, 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 6.8%. Calculate the z value for the test statistic.

A) z = 1.12

B) z = 1.09

C) z = 43.56

D) z = 1.35

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 4.1%, 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 6.8%. For a level of significance of 5%, what should the researcher’s decision rule look like?

A) Reject H₀ if z is less than or equal to -1.96.

B) Reject H₀ if z is greater than or equal to 1.96.

C) Reject H₀if z is less than or equal to -1.645.

D) Reject H₀ if z is greater than or equal to 1.645.

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 4.1%, 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 6.8%. What should the researcher’s conclusion be for a 5% significance level?

A) We reject H₀ at the 5% level because 1.35 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 4.1%.

B) We fail to reject H₀ at the 5% because 1.35 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 4.1%.

C) 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 4.1%.

D) We fail to reject H₀ at the 5% because 43.56 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 4.1%.

Question

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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 4.1%, 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 6.8%. The researcher’s hypothesis, for a level of significance of 5%, should resemble which of the following sets of hypothesis?
A) H₀: p > .041; H₁: p = .041; alpha= .05
B) H₀: p > .041; H₁: p = .041; alpha= .95
C) H₀: p = .041; H₁: p > .041; alpha= .05
D) H₀: p = .041; H₁: p > .041; alpha= .95

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 4.1%, 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 6.8%. Calculate the z value for the test statistic.
A) z = 1.12
B) z = 1.09
C) z = 43.56
D) z = 1.35

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 4.1%, 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 6.8%. For a level of significance of 5%, what should the researcher’s decision rule look like?
A) Reject H₀ if z is less than or equal to -1.96.
B) Reject H₀ if z is greater than or equal to 1.96.
C) Reject H₀if z is less than or equal to -1.645.
D) Reject H₀ if z is greater than or equal to 1.645.

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 4.1%, 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 6.8%. What should the researcher’s conclusion be for a 5% significance level?
A) We reject H₀ at the 5% level because 1.35 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 4.1%.
B) We fail to reject H₀ at the 5% because 1.35 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 4.1%.
C) 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 4.1%.
D) We fail to reject H₀ at the 5% because 43.56 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 4.1%.

Accepted Answer

From the given data:
p^=0.068n=98
 
a) Null and Alternate hypothesis:
H0: p=0.041
H1: p>0.041…